Analysis is always an interpretive act, meaning there's not always a definitive answer, but rather an answer that, based on the evidence, is the best fit.
As I hear the piece and watch the analysis, there's one main feature that suggests it begins in B minor and not D major: because B minor returns several times elsewhere in the piece. See 2:20, 3:10 (in B major), 4:08, 6:13, etc. In fact, almost the entire second half is based in B minor.
Throughout much of music history, tonal composers have had a preference for monotonality, which basically means beginning and ending in the same key. Since m. 8 here is the beginning of this section, the analyst is probably choosing B minor instead of D major to show that monotonal relationship. And since B minor is present for over half of the piece, it's pretty clear that B minor is the overall tonality.