Three remarks:

I. About the opening stage. - R. Fine, "Practical Chess Openings", reprint, New York 1973, p. 148: "The [opening] line, with which Alekhine broke the deadlock in his match against Capablanca, has never never been refuted, and it is not clear why it has not been played since."

II. About the middle game stage. - A. Alekhine, "Alexander Alekhine's Best Games", algebraic ed., London 1996, p. 140: "If White [at his 32nd move] wants to play for a win he is compelled to give back (at least temporarily) the extra pawn. But a more efficient and, taking into consideration his two last moves, logical, method of doing it was 32.a6!. After 32...bxa6 (32...b6 33.Bb8) the reply 33.Ra1! would have prevented 33...g5 because of 34.hxg5 Bxg5 35.e4+!, while after 33...Rxb2 34.Rxa6 Rb7 35.Ra5 White's positional advantage would become decisive."

Game Collection: Sting in the tail in pawn races: skewer, check

Position after 63 ... h3-h2 64 f7-f8= h2-h1= 65 f8-a8+ <skewer>

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At first I did not understand why Alekhine did not <BLOCK> the defending Black f3-rook with h7-h6-f6. But the ending makes this point clear: Alekhine wants his rook to be taken on f5 and not f6 (62 ... f3xf5) so that he can recapture with the White e4-pawn (63 e4xf5), thereby opening the a8-h1 diagonal for the <STING IN THE TAIL> 65 f8-a8+ shown above.

So in the positions prior to the one given above Alekhine was already thinking about how to exploit the tactical nuance that the Black c6-king was <LINED UP> with the h1-promotion square of the Black h3-passed pawn!

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after 63 ef 1-0 !

it needs some explanations :

Asian Youth 2011
R9 14-Under G/90
Tachaplalert of Thailand vs Sol Cruz of Philippines
1 d4 d5 2 c4 e6 3 Nc3 Nf6 4 Bg5 Nbd7 5 cxd5 exd5 6 e3 ...

However, Black continued with 6... h6 instead of Capablanca's 6... c6.

The game ended in a draw on move 45.

1) trade pawns on d5;

2) develop white king's knight to e2;

3) attack with pawns on the king's side and try to castle queen's side.

Alekhine implemented most of the above -- but Capa stopped him from castling at all , at the cost of a pawn. Alekhine's own notes in fact preferred 18 Bxd6 Nxd6 19 0-0-0 as a more promising attacking line than the game continuation.

Ok, now white has 3 options
1) 30.exd5 Bd6! 31.Be5 Rd2! and active pieces guarantee black even without two pawns easier defense than what actually happened in game. Comp evaluation after couple of moves approaching 0.00.

2) 30.a4 (trying to activate rook after advancement of pawns) Re2 (Ke6 is also interesting, but not sufficient) 31.exd5 Bd6 32.a5 (32.b4? Rd2!)Bxf4+ 33.Kxf4 Kd6 Again, position without 2 pawns, but comp easily draws rook ending after 10-15 moves. Main criteria here is active black pieces. It is true that from human point of view it is quite difficult to go such types of positions.

3) 30.Rc1! (best try for white) Rxb2 31.Rc7+ Ke8 32.exd5 Bd8 33.Rc8 Rxa2 34.Bc7 Kd7 35.Rxd8+ Kxc7 36.Rf8 Kd6 37. Rxf7 b5 38.Rf6 Kxd5 (alternate 38...b4 is also very interesting) 39.Rxg6 b4 40.Rh6 b3 41.g6 Ra1 42.Rxh5+ Kxd4 (42..Kc4? 43.Rg5!) 43.Rb5! Rg1+ 44.Kf4 Rxg6 45.Rxb3 a5 I am not sure, but this looks closer to win for white than draw for black. This rook ending was best try for white after the possible variation until move 40.

Anyway last actual mistake was 34..Bxd4 instead of much better 34..dxe4.