backrank: When Black took the pawn a2 (26. ... Qxa2) he certainly relied on the reply (27. Ra1) Rxd6!? (27. ... Qc2 28. Be4). He had either overlooked that on 28. Qe5 he can't play f6 because of 29. Qd5+!, or that after the text move 28. ... Qd2 the Bb5 is hanging.
So, 26. ... Qxa2 had cost a piece, and had White played 30. Bf3 (the safest way to defend f2; note that 30. Rf3? Rxf3 31. Bxf3 Qc3! would unvoluntarily have returned the piece!), the remaining moves wouldn't have been of any interest.
However, White decided on concluding the game with a mating attack which he considered quicker.
After 32. Raa8 he probably expected Black to resign! Instead Black found the clever resource Kg7, after which White couldn't take on f8 if he didn't want to get mated himself (on e1).
After 34. ... g5 (better Rb6 which would have put on a very hard resistance), White doesn't take on c4 since the resulting endgame with the pawn f2 missing would be extremely difficult to win (in spite of the extra piece), but continues the mating attack. Chekhover, a notable endgame composer, performs this task with vigor and artistry.
From move 35 on, his play is flawless and extremely instructive. White's problem is that his extra piece, the Bg2, can only move with check if he doesn't want to be punished by Qf1#. Furthermore, he must always keep an eye on e1 (or his back rank, in general).
Now he weaves a mating net around the black king.
35. g4! threatens Qf8+ Kg6 Be4+. Black's clever reply relies on 36. Qf8+ Kg6 37. Be4+?? Rxe4! (again the weakness of the white back rank!).
Now comes the most important point of that stage of the game: White realizes that he must achieve the same position as after White's 35. move, BUT WITH THE WHITE QUEEN ON e7. This would rule out Black's reply Rf4 (due to Qxg5#).
And it's indeed possible to achieve the desired position, as the game continuation shows. Black's alternatives on moves 37 and 38, resp., lose quicker than the text (e.g. 37. ... f6 38. Rg8+ Kf7 39. Bd5#,; or 38. ... f6 39. Qe7+ Kh6 40. Rg8 Rxg4 41. Qg7+ Kh5 42. Qxh7#). From move 39 on, the rest is forced (note that White manoevers so that he always controls the critical square e1 by at least one piece), and the game is over in exactly the moment where the extra piece on g2 would enter the battle by a check on d5 or e4 (45. ... Kg8 46. Bd5+ Kh8 47. Qf8# or 45. ... Kh6 46. Qf8+ Kg6 47. Be4+).