Jgamazo: Morphy fought for the initiative in all his games. 5.d3 is not in the spirit of the opening, unless your Karpov.
After 6.h3 De Riviere gives up the initiative to prevent Bg4 which isn't a real threat. Morphy plays 6. ... h6 to prevent Ng5, which is a real threat. Some may prefer to castle here 6. ... 0-0 7.Ng5 h6 8.Nxf7 Rxf7 9.Bxf7+ Kxf7 Black exchanges rook and pawn for bishop and knight which is roughly equal. I prefer Morphy's choice.
9.Na3? De Riviere's plan to get his knight to d5 or f5 was too slow,
9.0-0 was better.
The second point about Morphy's games is his rapid development, on 10. ... Be6 he was castled and started tactical manoeuvers.
11. ... d5 opens the center, the third component of Morphy games.
13.0-0 De Riviere castles to avoid the storm in the center, but 13.Bxd5 Qxd5 14.c4 Qe6 maybe preferrable. Morphy respondes by more center opening 13. ...e4.
De Riviere plays 16.c4 to fight for the initiative but 16. ... Ng3! is nicely played, forking Queen and Rook.
18. ... Ne7?!, better was 18. ... Ncd4. 20.Rxe7 puts a rook on the 7th, De Riviere must have felt he was in control...but 22.g3? losses the initiative, better was 22.Ra3 Nf4 23.Rxc7 with ideas like Rc3 and d6.
24.Ncd4?! a better try for equality was 24.Rf1, the f pawn was under pressure most of the game. If 24. ... Bxf2 25.Ng1 Rd2 26.Nf3 Re2 with equality.
White resigned, but there was no mate in sight. Black was better but there was still play in white's position, a possible continuation is: 25. Kh1 Nxb4 26.d6 Bxd4 27.Nxd4 Nd5 28.Rxb7 Rd8 29.Kg1 Rf6 30.d7 Rd6 black is slightly better.