That said, your link's observation that it's a curated list actually means that it is more of an accolade than merely sales. It means that somebody at the Times wanted the book on the list, which says more to its readers.
It's not much, but when you're trying to stand out in a crowded market, each little bit helps. Popularity has a positive feedback effect, and it's really slow going if you can't take advantage of it. At least for a cycle or two.
Given the NY Times growing irrelivance in the market, the high-profile cases of having their list gamed more than once, their ongoing war against their own users with the 3rd party tracking and bullshit they pull over cancellations, I somehow doubt their list is having much of an impact on anyone.
I don't know how much that helped, but the underlying logic makes sense. He had a medium-sized niche audience, but their word of mouth wasn't going to sell a lot of extra copies. This put the book out on a world stage. And it just so happened that this particular book (a nerdy exploration of the politics of pre-Caesar Roman Republic) might appeal to the New York Times readership.
That's what the list could be for at its best: a mechanism for breaking out of your niche. I have no idea how many extra books it sold, but it was a meaningful mechanism for trying.
Why is that? Surely if both are well written/marketed enough they could both be bestsellers?