KEG: I entirely agree with tranquilsimplicity that games such as this one are a major reason to love chess.
This was a no-holds barred slugfest and a delightful miniature. Tchigorin played the Bishop's Gambit (the same opening that led to grief for Janowski against Bird back in Round 13 of this tournament), and Schlechter played the violent line with 4...Nc6 and then 5...Bb4 in lieu of the more solid (and theoretically better) 4...c6.
Tchigorin could have had a decent game with 7. d3, but he went for the jugular with 7. e5. My computer doesn't like this move, but I do. In any case, had Tchigorin played 7. d3 no one would remember this game!
Schlechter had the better chances until his 11...Ba5. He should have played 11...Bd2!, which would have required Tchigorin to trade off his f3 Knight--the piece that was to lead to Schlechter's demise two moves later.
The Tournament Book correctly identifies 12...Qxd6 as the losing move. Tchigorin was better after Schlechter's 11...Ba5, but 12...cxd6 seems to keep Schlechter in the game. After 12...Qxd6, 13. Ng5! was a powerful shot, and I see no way for Schlechter to save the game after this.
In any case, Schlechter should have played 13...Be6. This probably would not have saved the game for him, but it would have avoided the fireworks on f7 that followed Schlechter's disastrous 13...Qg6??
Andrew Chapman is correct that 14. Rxf7 was the best move. While Tchigorin's 14. Nxf7 also wins, 14. Rxf7 is murder.
After Tchigorin's 14. Nxf7, Andrew Chapman is again correct that 14...Be6 is best. It still loses to 15. Bd3, but at least it would have prevented Black from getting wiped off the board after 15. Ne7+.
Ron's proposed 15. Nf4 after 14...Be6 is a mistake. Black's Queen does not have to move here. Rather, Black can turn the tables and secure a clear win with 15...BxB! Then, if 16. NxQ d2 wins the house.
Schlechter's 14...RxN was immediately fatal. As the Tournament Book correctly notes, had Schlechter continued with 17...KxR then 18. Qh5+ wins the Black Bishop on a5.
As gandu so aptly sums up, "Nice game!"