The immediate cause of Black's defeat was the loss of his rook (and then he couldn't move his own pawns down the board fast enough to win back White's rook, but let's not spoil the narrative).

Why did he lose his rook?

--Because White queened his a-pawn.

Why could White queen his a-pawn?

--Because he'd won Black's a-pawn.

Why could White win Black's a-pawn?

--Because Black had weak pawns on d6 and a6 and couldn't defend both.

Why did Black have weak pawns on d6 and a6?

--Well, the two weaknesses are related. The a-pawn is weak because White's king can reach it via b5.

But why can the White king reach b5?

--Because Black's king is (for a long time) imprisoned on d7 by the White pawn on d5 and its own pawns on d6 and c7. To break the bind, Black plays 52....c6, and after 53. dxc6+ he is saddled with the aforementioned weakness on d6.

But why is there a White pawn on d5?

--Because Black played 37....BxN(d5) and White retook with the c-pawn.

Why did Black play 37....Bxd5?

--Because there was no other way to save the isolated, doubled pawn at f6.

Why was there a doubled, isolated pawn on f6?

Because of 12....Qf6.

Q.E.D.

That said, Saint/Rabbi Emanuel forbid that anyone should say that there's nothing Black could do differently between moves 12 and 91. I don't think he should have traded rooks on move 48, for example. You might query 25....b5 and 26....a5, since they lead to the isolated pawn on a5. On the other hand, 14....Bg4, to rid the board of White's knight, doesn't seem to work: 15. Bxc6 Bxf3? 16. Bxb7 Bxg2?? 17. Rhg1.

The one thing I am sure of is that Black doomed himself to a very difficult defense when he played 12....Qf6. The weaknesses on the k-side influence the play even more than my little catechism above indicates. For example, even though Black has the "active" rook in the ending White's pawns are relatively easy to guard, while if White's rook ever gets loose among Black's pawns the game would be over in a hurry. That's another reason the Black king had to stay in the center and couldn't guard the a-pawn.

52...Rb2! [cutting off the white king] 53.Rb3 Re2 54.Kb5 [54.Kd4 Rd2+ changes nothing] Rxe4 55.Kxa5 Rd4 56.Rb5 Kc8 57.a4 h6! and White can do nothing.

Instead of 64...Ra4+ Black could try 64...d5 aiming for counterplay with his passed pawn.

However it seems to me that 65...Rf4 is the losing move, where 65...Re4 would still have drawn. The difference is that after 66.Rc3+ Black can just play 66...Kb7, whereas in the game 66...Kb7 would lose to 67.Re3 with the threat of 68.Re7+.