The difference is that his product does not compete in with the New York Times; it may be valuable to the Times' competitors, but nobody will watch his video and then not read the Times article as a result. The criteria for judging fair use include the potential impact on the market value of the copyrighted work; in this case, it seems that the impact is basically nil, because there are two separate markets. It is not about commercial intent, but rather about the effect in a particular market (and even that is not cut-and-dry).

The case of textbook publishing is different, because the copies compete with the original in the same market.

Really though, my point was not about the educational nature. Even if we assume there is no educational value to the video, it is still a case of criticism/commentary, which is still fair use. The author is not in any way reducing the value of the Times article. The article was not copied in full. These are all things that support the claim that this is fair use.

While commercial interest is a factor in the determination of fair use, it is not an automatic disqualification of the defense. Negative reviews, for example, are generally protected by fair use, including when there's a commercial interest behind them.