AylerKupp: Interestingly, there are 6 games in the chessgames.com database with the position after 10.Be4 and it shows one win for White (this game), 3 wins for Black, and 2 draws. In the chesstempo.com database there are 12 games with one win for White (not this game), 5 wins for Black, and 6 draws. So, statistically speaking, 10.Be4 did not work out well for White.
In all games except the 2 wins by White one Black continued with 10...f6 instead of 10...e6 or 10...f5. Lynch's 9...Bg4 pretty much commits Black to exchange his LSB for a knight so Fischer's 13.Bxc6 wrecks Black's pawn structure and after 15.Rxf3 Fischer seems to have a much superior position.
Fischer's 17.Nxd5 was surprising to me, straightening Black's pawn structure somewhat, but both Black's c-pawn and e-pawn remain backward, the e-pawn on a semi-open file, and Black has no counterplay. And after 21.Be5 Bxe5 22.Rxe5 Black is pretty much restricted to passive defense.
Fisher's 35.g5 was also surprising to me, given that White's rook is pinned. After 35.Kg2 the g-pawn is free to advance and after 36.g5 hxg5 37.hxg5 Black's Pe6 falls and Black will either be subjected to a mating attack if he doesn't exchange pieces or a lost K+P ending if he does.
Finally, I question the wisdom of 39.a5. White could support the b-pawn's advance with either 39.Qc3, 39.Qd1, or 39.Qd2, and prevents any Black counterplay via ...Qb4. 39.a5 does prevents any Black counterplay against the Pd4 by ...Qb6, but now obtaining a passed a-pawn requires a pawn sac.
Yet I am not too perplexed with Black's resignation. On the surface it seems that all that White has to do is advance the b-pawn after 40.Qc3, 40.Qd1, or 40.Qe1 and the resulting passed a-pawn looks pretty much unstoppable. If Black tries to stop it he will lose the Pe6 and subject himself to a mating attack.
But all is not what it seems if Black has the courage to abandon its Pe6 and try active defense. After 39.a5 Houdini at d=29 indicates that Black has a draw by repetition after 39...Qc7 40.Rxe6 Rxe6 41.Qxe6 Qc1+ 42.Kg2 Qxb2+ 43.Kf3 Qc3+ 44.Kg2 Qd2+ or after 39...Rh8 40.Qf3 Qe7 41.Qxd5 Qc7 42.Qc5 Qf7 43.Re1 Rh1+ 44.Kxh1 Qf3+ 45.Kg1 Qg3+. I particularly like the second line; a simul player doesn't often get a chance to successfully sac a rook against Fischer! Neither Stockfish 2.2.2 at d=33 nor Rybka 4.1 at d=24 can find anything better for White than a draw, although neither finds the rook sac. However, Black has been tied to passive defense for many moves defending his backward Pe6 and it was probably too much to expect for a typical simul player to switch gears, abandon the pawn, and possibly sac a rook against Fischer to obtain the draw.
And I tried 39.Qc3, 39.Qd2, and 39.Qe1. But Houdini at d=28 couldn’t come up with anything better than a draw by repetition after any of those 3 moves, and White has to be careful not to allow Black any k-side counterplay. For example, after 39.Qe1 Qd7 40.b3 Qf7 41.Qe3 (to try to prevent 41...Qf4), Houdini evaluates the position at [-2.36], d=29 after 41...Rf8 42.Qe1 Qf4 43.Re3 Rf5 44.Rg3 Qxd4+ 45.Qe3 Qxe3+ 46.Rxe3 Rxg5+ and Black is two pawns up.
So, if Black had had some courage (not easy against Fischer!) and the ability to switch gears and go into active defense, he should have been able to force a draw.