KEG: A devastating attack by Mieses overwhelms Tchigorin, but there were some bumps in the road before that and Tchigorin definitely had his chances.
White could maintain a small edge with 5. Nf3, but that was hardly Mieses' style.
Carrying on with his dubious but dangerous attacking plan. 6. Nf3 was theoretically best.
As Schlechter notes, Tchigorin's intention of exchanging on c4 only helps White. Schlechter's suggested 6...Nd4 is unquestionably better than the text, though 6...h6 may be even stronger.
Reckless, but once again very much in Mieses' style. 8. Bb3 was theoretically best.
Missing his chance. As Rosenthal notes in the Tournament Book, 8...h6 is best.
Tchigorin managed to trade Knight for Bishop on c4 on move 9 as planned, but now sees he has little to show for this exchange. To maintain any edge from Mieses' dubious king-side advances Tchigorin needed to play 11...d5 here. With the text, he gets a bad game.
It is hard to understand Tchigorin's thinking here. 13...0-0 would have avoided most of the troubles he soon faces.
Rosenthal gives this a "!" in the Tournament Book, but the move in fact is a mistake. Best was 14. Nf3.
This could have been the losing move, had Mieses followed up properly. 14...Nd7 was best.
Schlechter correctly notes that 14...a5 would lose to 15. Be3. The Tournament Book (i.e., Rosenthal) is also correct that 14...d5 would have been bad here, but not because of 15. Ba3 because 15...Qxg5 is sufficient (Rosenthal's claim that this would lose to 16 Qxe5+ is nutso). Rather, 14...d5 would lose to 15. cxd5, since 15...cxd5 loses to 16. Nf3.
15. gxf6 was much better.
Suicide. Rosenthal claims that this move in "in accordance with Tchigorin's temperament." And indeed passive play was not his thing. But 15...g6 is reckless. Rosenthal recommends 15...Bd7, but this is almost as bad as the text, since 16. a5 Nc8 17. Rg1 would follow. Best, and offering reasonable chances of resistance, was 15...Nd7. After the text, Mieses makes short work of Tchigorin.
Rosenthal claims that 17...Qf7 was better, but he only considers 18. f6 which gives Black chances (18...h6) whereas 18. Nxe5!! is crushing. Relatively best for Black here was 17...Qf8, hardly sufficient but keeping his hopes alive by keeping an eye on the d6 pawn.
Even better than 18. 0-0-0. Mieses plays the final stages of this game brilliantly.
Now the roof falls in and the game ends quickly and violently. The only hope of prolonging the game was 19...Bg4.
"A very pretty move which concludes the game brilliantly" (Rosenthal in the Tournament Book).
As HonzaCervenka points out, 23...Kh7 loses (see the line in his post). Resignation here was thus entirely warranted.
23. Rxg6+ also wins, and in fact leads to a forced mate.