And now about Nakamura's other tweet: It may well be that Nakamura enjoys his (numerous and/or "active") fans and doesn't care about those who like him less, let alone those who consider and call him a "prick". Note that I never did, and never will use such language about Nakamura or anyone else - even if I to some extent understand the underlying reasons. Of course that tweet could also be just a compliment to himself ... .

It isn't just about whether Nakamura should or shouldn't have played Tal Memorial, but also about his general reputation in "Soviet" chess circles (which I frankly don't know). As to his invitation: organizers emphasized Elo - where I would put him in the second group with Caruana, Radjabov, Morozevich and Grischuk, it doesn't mean too much that he happened to be second in that group and fifth overall, just a few points give and take. BTW they didn't use (only) Elo to select the Russian players, else Karjakin would have participated.
People commenting emphasized his bad result at Tal Memorial 2011. At least the Dortmund organizers take previous results in their event into account, and had announced that the two bottom finishers won't be re-invited straight away. They made an exception for Georg Meier due to a fully legitimate deal with the German federation. Next year it will be easier for them: Gustafsson will probably only be re-invited if they repeat the same format (which, as far as I know, hasn't yet been decided). And Bartel will only be re-invited if he wins Aeroflot again, or maybe if he (even less likely?) gains 50-100 Elo points in the near future.

A short and simple question which still gets a longer answer :) . First, engines (plural) was wrong: I referred to the live transmissions at Chessbomb and Whychess, and both use the same version of Houdini (2.0c x64) - at limited search depth, but it might still see as much as or more than any GM at the board. I did not refer to own engine usage.
My point wasn't to question your game coverage - in that respect sorry for using the wrong words. But the line 29.-hxg2 30.Kxg2 Nh3!? 31.Bxg3 looks at least a bit scary for white. In some cases, black would sacrifice a knight to reach such a position (which he did in the game by burying his Nb8). So the real question is whether Nakamura would have kept things under control. The video doesn't answer this question as he merely says "29.Qd2 now it's completely winning" - which could mean two things: he did see the above-mentioned idea, was ready to face it and optimistic about his chances ... or he didn't see the entire idea. And apparently the interviewer Klaus Bischoff didn't use an engine?

And it was all in the context of some earlier games by Nakamura where he grabbed tactical chances in worse, dubious or objectively lost positions. Though "turnaround" is also too strong in the given case. Bacrot might have kept some practical chances, whereas in the game his position was completely lost (=resignable) in just a few more moves.