Jgamazo: Morphy plays both sides of the Guioco Piano. I think he played this against his toughest opponents; Charles Henry Stanley was the first US Chess Champ.
5.d3 I prefer 5.d4 to take the initiative.
6.h3 prevents a knight getting to g4 to attack the f pawn, but 6.0-0 was better.
7.Bg5 If your not going to take the knight why play this move? 7.b4 Bb6 8.a4 a6 9.a5 Ba7 10.0-0 Carving out some queenside space was better.
8.Nbd2 White brings his knight over to the kingside for a possible attack.
8. ... Be6!? Morphy starts a plan to open the f file for his rook and Queen. if 9.Bxe6 fxe6 10.0-0 h6 11.Bxf6 Qxf6.
10.Bh4 White doesn't like that plan, but he could still take the bishop and play this next.
10. ... Kh8 the plan changes, this prepares g5 and Rg8. 10. ... Qe7 was also good.
11.Nh2? This plan to get his knights on the kingside is premature and ignores Morphy's next move. Better was 11.Bb5 Ne7 forcing the knight to block the Queen. 12.Bxf6 gxf6 and forcing a pawn capture to keep the f file closed and keeps the queen out of the kingside.
11. ... g5 How did White miss this?12.Bg3 Forced
12. ... h5 going after the bishop, but 12. ... Qd7 attacking the h pawn might be better.
13.Nhf3 forced or lose a bishop. This is why 11.Nh2 was bad.
13. ... h4 leaves the g pawn hanging. 13. ... g4 is slightly better.
14.Nxh4? Better is 14.Bh2 or why play 13.Nhf3 the move before.
15. ... Kg7 plan change again, 15. ... Rg8 is good too.
16.Qf3 heading to g3 to attack the black king.
16. ... Rh8 more pressure on the h pawn.
18.Qg5 threatens to take the knight and queen but...
18. ... Nd7 evens the trade.
20.Qxd8+ Also good was 20.Nf3, but black is still in command.
23.Kg2 objectively best, but black is still better, so why not try 23.Bxd8 Rxd8 24.a4 complicating. From now on White can not improve his game unless Black blunders.
24.Bg5? or 24.Bg3 Nc6 25.h4 Raf8 26.Ng5 Rf6.
25.h4 or 25.Bd2 d5 26.rae1 Rad8 27.d4 exd4 28.cxd4 e5 29.dxe5 dxe4 30.Rxe6 Nfxe5.
26.hxg5 or 26.Nxg5 Rxh4 27.Nxe6+ Kf6 28.f4 exf4 29.Nd4 Rxg4+ 30.Kf2 Ne5 31.Rad1 Bxd4+.
27.Kg3 Why not resign? No help was 27.Kg1 Rh3 28.Rfd1 Rah8 29.Kf1 Rxf3 30.Ke1 Rxf2 31.d4 Re2+ 32.Kf1 Rh1#