This is a situation in which inadequate understanding of terminology causes confusion.
In the referenced text, the Jews are called Adam, and the Gentiles are not called Adam. The Gentiles are the non-Jews. Adam literally translates to "Man" (hence its appearance in DevSolar's answer).
So the people who claim that it supports considering the non-Jews to be beasts are basing it on the literal translation...
... but the literal translation is incorrect, because context matters.
When referring to human vs animal, the term Bnei Adam is used, which means "Sons of Adam" (in this case, referring to the Adam of "Adam and Eve").
In this situation, "Adam" is actually referring to the people of Israel collectively as though it is a single being. And in the context, what it's saying is that the rituals are for the people of Israel (the Jews), not for the Gentiles.
For more information, see here.
One can see the actual context, with explanation, in another way, here. Notice that it is speaking of purity of dwellings. The Talmud is guidance, more akin to the Hadith of Islam, as opposed to the Torah, which is like the Quran. As such, much of its contents reference things found in the Torah. In this case, it's referencing usages of "man" such as that found in Numbers 19:14, which says "If a man dies in a tent". The source here clarifies that "man", here, only applies to Jews.
Also note that the phrase "They are beasts" (or rather, the equivalent in Talmudic Aramaic) does not appear. This phrase is a fabrication, added by those who wish to demonise Jews.