The words of this out of context quote are correct, the origin for this quote in terms of authorship are correct, the origin in terms of attributed time are not correct.
Both, misattribution of time and lack of context, make this essentially correct quote problematic.
According to David Ben Gurion's 1954 book Rebirth and Destiny of Israel he wrote an essay in 1917 called "In Judea and Galilee", in which he wrote about Zionist settlers:
"We were not just working--we were conquering, conquering, conquering land. We were a company of conquistadores."
More easily accessible in Joseph Schechla: "Forced eviction as an increment of demographic manipulation", Environment and Urbanization, Vol 6, Issue 1, 1994.
Since this quote is often used in anti-Semitic contexts or other undesirable venues, it seems quite necessary to point out that while the quote is correct, although wrongly attributed concerning the exact date, the quote does not reflect the reality of 1917 at the time in the land and might need further context and explanation. The context is that a nationalistic (zionist) warringly and worryingly romanticising Ben-Gurion militarises Jewish settlement struggles, both against the harsh nature of the land as well previous inhabitants. This martial sounding and heroic language is typical for the time of writing for many authors and represents an invitation for misunderstandings. Which of these struggles, against "nature" or "natives" are most emphasised are up to debate, but over time his attitudes and actual policies changed.
The land, he believed, must be conquered by the toil and sweat of Jewish pioneers, not by force of arms.
From: David Landau: "Ben-Gurion: A Political Life", Schocken Books: New York, 2011.
This much less aggressive stance is evidenced in praxis later:
Allon’s support for such a conquest, which would have delivered into the hands of the tiny Israel of 1949 the same West Bank Arab population that it found so hard to digest – nay, that it was unable to digest – twenty and forty years later, was very probably one of the reasons for Ben-Gurion’s refusal to appoint Allon and others of like mind to key positions in the post-1948 Israel Defense Forces.[…]
At the end of the war, when Yigal Allon, who represented the younger generation of commanders that had grown up in the war, demanded the conquest of the West Bank up to the Jordan River as the natural, defensible border of the state, Ben-Gurion refused. He recognized that the IDF was militarily strong enough to carry out the conquest, but he believed that the young state should not bite off more than it had already chewed.[…]
At the same time, Ben-Gurion was concerned that if Israel attacked Jordan, a European power, Britain, might intervene. He had no territorial aspirations: “At this stage we are not short of territory, but of Jews. And conquest of additional territory will not add Jews, but Arabs,” he wrote to a young man who proposed that he take the West Bank.
From: Shlomo Aronson: "David Ben-Gurion and the Jewish Renaissance", Cambridge University Press: Cambridge, New York, 2011.
This realpolitik approach is evidenced almost as early as the quote in question:
In 1918, David Ben-Gurion explained:
The true aim and real capacity of Zionism are not to conquer what has already been conquered (e.g., land cultivated by Arabs), but to settle in those places where the present inhabitants of the land have not established themselves and are unable to do so.
From (Ben-Gurion 1973, written in 1918 and first published in Der Yiddisher Kempfer), cited from: Daniel E. Orenstein: "Zionist and Israeli Perspectives on Population Growth and Envirnomental Impact in Palestine and Israel", In: Orenstein, D.E., Miller, C. and A. Tal (eds.): "Between Ruin and Restoration: Chapters in Israeli Environmental History", University of Pittsburgh Press: Pittsburgh, 2013.
To determine the source of this claim and quote it might be useful to watch the video from the question just a few seconds longer and wait for the next quote attributed to Ben-Gurion:
"We must expel Arabs and take their places"
Then compare this to Wikipedia's version:
"We do not wish, we do not need to expel the Arabs and take their place. All our aspirations are built upon the assumption — proven throughout all our activity in the Land — that there is enough room in the country for ourselves and the Arabs."
Letter to his son Amos (5 October 1937), as quoted in Teveth, Shabtai, Ben Gurion: The Burning Ground; and Karsh, Efraim (2000), Fabricating Israeli History: The 'New Historians'; this has been extensively misquoted as "[We] must expel Arabs and take their places" after appearing in this form in Morris, Benny (1987), The Birth of the Palestinian Refugee Problem, 1947–1949, Cambridge University Press, p. 25.