There seem to be two claims here. One is that there are no counterexamples of other cultures with a national tradition of a national divine revelation or miracle. The other is an implicit claim that Judaism itself does have such a tradition.
Claim that Judaism has an unbroken national revelation tradition
In terms of whether Judaism itself has such an uninterrupted nation-wide tradition of the entire nation hearing God directly speak the Ten Commandments, as Kelemen claims, it seems only partially true going by the biblical narrative.
First, it does appear as he says that the biblical narrative includes the Jewish nation experiencing national miracles and at Mt. Sinai hearing God speak, though this latter detail is not obvious from the narrative. Some verses do say that the Jewish people heard God directly, for example:
Face to face, the Lord spoke with you at the mountain out of the midst of the fire. (Deuteronomy 5:4)
For who is there of all flesh, that hath heard the voice of the living God speaking out of the midst of the fire, as we have, and lived? (Deuteronomy 5:22)
But at the same time, other verses may conflict with this. For example, Exodus 19:21-25 has God allowing only Moses and Aaron up the mountain to see God and receive the commandments, but nobody else could even touch the bottom of the mountain. The people, according to Exodus 19:18-19, simply saw fire, heard loud noise, and possibly heard the voice Moses was conversing with. Deuteronomy 5:5 appears to make Moses the intermediary when God delivers the Ten Commandments.
It seems that the view that all Jews directly heard God did become the accepted position among rabbinic leaders, however. For an example, Rashi on Exodus 20:2 says:
...Alternatively, [God mentions the Exodus] since they [the Israelites] heard many voices [during the revelation], as it is said: “And all the people saw the voices” (verse 15), [meaning that] voices came from four directions and from the heavens and from the earth...
Even if it's not clear whether the people were supposed to have heard God speak directly, Deuteronomy 11:2-7 does describe various national miracles, such as the splitting of the Red Sea. Kelemen may have been better served using one of those other miracles as his main example. It is clear that according to the Torah the Jewish people did witness at least some nation-wide miracles, but whether the people were supposed to have all heard God speak directly in the way Kelemen says is not as clear.
Nation-wide unbroken tradition
Whether the biblical narrative includes an unbroken chain of tradition about Mt. Sinai is a different story. There are various places in the Hebrew Bible that describe periods of time when the Jewish people apparently rejected and/or forgot their religion for Canaanite religion en masse, for example:
And also all that generation were gathered unto their fathers; and there arose another generation after them, that knew not the LORD, nor yet the work which He had wrought for Israel. And the children of Israel did that which was evil in the sight of the LORD, and served the Baalim. And they forsook the LORD, the God of their fathers, who brought them out of the land of Egypt, and followed other gods, of the gods of the peoples that were round about them, and worshipped them; and they provoked the LORD. And they forsook the LORD, and served Baal and the Ashtaroth. (Judges 2:10-13)
Further, a reading of II Kings chapters 21-23 describes a 75 year period where Canaanite religion was national and Torah was apparently unknown before being discovered under King Josiah who implemented major religious reforms and restored monotheism (known to scholars as the Deuteronomic Reform). Medieval Jewish commentator Rabbi David Kimhi (RaDaK) describes the state to which the Jewish people were unfamiliar with the Torah and its contents:
Manasseh had systematically destroyed all the Torah Scrolls and alienated the nation so thoroughly from the Torah that the people were completely unfamiliar with its contents. Sixty-seven [sic] years had elapsed since the beginning of Manasseh's reign, so that this discovery was a surprising revelation to everyone. (The Stone Edition Tanach, The Artscroll Series, citing RaDaK on II Kings 22:8)
So the biblical narrative does include later reintroduction of the Torah to the Jewish nation, and there appears no reason to say that the Mt. Sinai story was excluded from what the people had forgotten. It may be arguable whether an elite few always held on to tradition, but this is not Kelemen's claim. Going by the Hebrew Bible, Judaism does not seem to claim an unbroken nation-wide tradition of the Mt. Sinai events as Kelemen says and his implicit claim in this regard is false.
Note: This is not to say anything of the actual authorship of the Torah and origin of the the Mt. Sinai story. Whether a king made it up as part of a religious reform and told people it had been forgotten, whether it was the product of natural mythological development and embellishment over centuries, whether the Biblical narrative is completely accurate, or whether it is from some combination of the above, it does not change the reality of the resulting biblical narrative and Jewish beliefs. Whatever the history regarding the Egyptian exodus and Mt. Sinai, the biblical narrative does involve the Jewish people forgetting and being re-introduced to monotheism and the Torah.
Claim of no counterexamples
The claim that there is no other example of a culture with mythology of a national supernatural experience is quite an ambitious one as it would require an analysis of a huge range of beliefs of present and past cultures to verify that there were no other examples. However, there indeed are examples of cultures with myths comparable to the Mt. Sinai tradition, in the sense that these people believed all of their ancestors experienced supernatural events or witnessed their deity speaking:
Aztec Huitzilopochtli Myth and revelation of Huitzilopochtli: The Aztecs, who settled in Lake Texcoco, believed themselves to be descended from tribes of immortal people from Aztlan until they had to leave as instructed by their god Huitzilopochtli who took the form of a white eagle. The journey took 200 years and the ultimate destination of the lake on which they built an artificial island was prophesied in advance and in detail. Whether the Aztecs believed their god to have spoken to all the people or just a prophet is not clear from what I've seen. However, the story does involve all Aztec ancestors experiencing supernatural events, that is, the supernaturally long lifespans. Additionally, this story is an important aspect of the origin of Aztec religion. (source)
Fifth Creation of the World by Marumda and the Pomo tribes: The Pomo people, a group of tribes in California that exists today and had settlements dating back several thousand years, have an oral tradition that their god, Marumda, created the world five times (the first four destroyed due to sin), and that they were created the fifth time. They believe all of the Pomo villages were planted by Marumda and that he revealed themselves to their ancestors, sometimes accompanied with miracles, and taught them how to survive and behave and taught them dances that are still performed today. This story does involve national miracles as their god Marumda created their villages, it does have Marumda performing public miracles, it does have their god speaking to the people, and it does tell the story of the origin of their religious beliefs. What the size of the initial population that Marumda created and was revealed to was, and whether Marumda spoke to the entire nation at once or only to individual groups, is less clear. (source)
Revelation of Gitche Manitou at Pipestone, Minnesota: Sioux Indians have an oral tradition of a majestic, direct, divine revelation of their god and creator Gitche Manitou or the Great Spirit at the Pipestone National Monument to all the Native American tribes or to all the tribes in the region. In one account, in the form of a poem by Henry Wadsworth Longfellow based on legends, Gitche Manitou breathed into a peace pipe he formed and made a large smoke signal that beckoned all the tribes to gather. They had spite between them, but Gitche Manitou chided them to do away with their weapons, behave properly, and make peace. After this, before all the nations, Gitche Manitou ascended to heaven amidst the smoke. In another, less embellished account recorded by George Catlin from the Dakota Sioux, a detail is included that the Great Spirit was in the form of a large bird, smoke signals are not specified (instead smoke is described as rolling over the multitude), and the description of his ascent to heaven is not included. In both accounts though, the fundamental points of the revelation are consistent. This story does have a lot of similarities with the Mt. Sinai story, though details in the poem by Henry Wadsworth Longfellow may imply that it was only all the men or warriors as opposed to every member of the tribes. (Although, certain details in the Biblical accounts of Mt. Sinai also are directed only to men.) (source 1), (source 2)
The Lakota legend of White Buffalo Calf Woman: The Lakota People are a subset of the Sioux. In 1805 their population was estimated to be about 8,500 (and today there are tens of thousands of their people who speak the language). The people have an oral tradition of an event that took place one summer between year 12 and 10 BCE (according to this retelling) when their god Wakan Tanka (same as Gitchie Manitou) revealed itself to all seven tribes of the Lakota as White Buffalo Calf Woman. The story goes that there was famine, so all seven Lakota tribes gathered together, and they sent out two hunters to look for food. The first part of the miracles was only witnessed by one survivor, but for context, they saw a beautiful woman, with clothes and an appearance than no ordinary human could fashion, floating towards them. One of the hunters desired the woman and was turned into a pile of bones amidst a cloud. The other hunter became afraid and prepared to shoot the woman, but she couldn't be harmed. She informed the hunter to return and have the Lakota prepare for her arrival. When she arrived, she taught the Lakota how to behave and perform all the sacred rituals. She gave them seven religious practices, including the sun dance and fasting. She talked to all the people and gave them advice, and gave them a sacred living pipe that is still guarded to this day. As she left, the people saw her turn into a black buffalo, then brown, then red, and then white, which is sacred. As she disappeared, large herds of buffalo appeared where she was and allowed themselves to be killed for the Lakota to live. This story also meets a lot of Kelemen's criterion, it does tell the story of the origin of their religious beliefs, and the tradition is very strong. (source)
Samaritans: The Samaritans are a small ethnic religious group living in the Levant. They practice Samaritanism, a religion related to Judaism which is based off of the Samaritan Pentateuch as the sole holy book, which is an alternate version of the Five Books of Moses that includes some textual differences from the Torah, including the unique command within the 10 commandments to build an alter on Mount Gerizim. While Jewish sources consider the Samaritans to be foreign settlers from the Assyrians, Samaritans believe that they, and not the Jews, have the authentic Pentateuch and the authentic lineage tracing to Mount Sinai. Of course, the national miracle and revelation traditions Samaritans hold traces back to the same traditions held by Judaism. However, they nevertheless constitute a different people with a different religion having a tradition of a national revelation starting their religion. (source)
There may be additional counterexamples too, such as the Epic of Gilgamesh (and related flood myths) or the Founding of Thebes by Cadmus if you say that Rabbi Kelemen's claim does not necessitate that a sizable group experienced the miracles (just that all of the people's ancestors experienced it).
Whether these counterexamples do disprove his claim may depend on how narrow Rabbi Kelemen's claim is understood to be. If he argues that other peoples should have all their ancestors experience miracles or interaction with their god, then it is easy to see these as counterexamples, and his claim would be false. If, however, he requires that the peoples must have experienced something that matches his understanding of a national prophesy of a large population as the start of a religion with a continuous chain of tradition to the verifiably known believers, then some counterexamples become more arguable. But by the same token the claim would be far less meaningful, and as discussed above it would even be doubtful that the stories in the Hebrew Bible actually meet such a threshold. With the less narrow understanding of Kelemen's claim, though, the Mt. Sinai story would not be unique in the way he says and the claim would not be true on those grounds.