Steakanator: This game is much more interesting than people are giving it credit for.Mieses's 16. ♗h4 is obviously bad; he was clearly fishing for 16... g5 17. ♗xg5 fxg5 18. ♕xg5+ ♔h8 19. ♗xh7 and a chance at the brilliancy prize. Tarrasch was never going to allow something like that.
Things were fine for Tarrasch until move 33. His decision to trade on d1 was playable, though I wonder if he wouldn't have enjoyed 33... h5 34. ♗xg4 hxg4 more. I guess the win isn't super concrete after 35. ♖c1 followed by c3-c4.
The real mistake, however, was 35... cxd5. Tarrasch wrote in <Dreihundert Schachpartien> that he should have just played the simpler 35... c5 36. d6 ♘d7 and life is good.
After that, things became pretty unclear, with Mieses trying to keep things complicated with 44. ♔h3. I guess he was hunting for further swindles, not wanting to just defend the pawn-down position following 44. ♖xa7 ♘xg4+ 45. ♔g3 ♖xa7 46. ♗xa7 ♘e5.
The last mistake was 45. ♔h4. Mieses could have kept going with 45. ♗g3, but it's far from an easy draw even still.
As for why he kept playing, I suppose he figured that if he had swindled Tarrasch once already, he might be able to do it again.