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Here 37.Rxh6 White sacrifices the exchange by threatening mate next. By move 43 Black had lost all pawns and the endgame was R+B+2P vs 2R. At move 80 Black liquidates by capturing the two white pawns in a deflection of the B/d4. Finally a R+B vs R ending results in a White victory.

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That's true but it is not yet so trivial for white. After 101.Kd3 Rc8 white has to outmanoeuvre black's defence with several accurate moves. One possibility is 102.Rf2 Re8 <[102...Ke1 103.Rf5 (with threat Bc3+) 103...Rd8 104.Rb5 Kf1 105.Rg5 and the game is over.]> 103.Bf6 <(covers d8)> 103...Re6 <[The only other move 103...Ke1 is not better: 104.Rf5 (with threats Bc3+ or Bh4+) 104...Kd1 (absolutely forced) 105.Rb5 Rc8 (if 105...Ke1, then 106.Bd4 Kf1 107.Rg5 etc.) 106.Bg5 Ke1 107.Rf5 and black has no defence against threatening Bd2+ or Bh4+ with mate.]> 104.Bc3 Rd6+ <(the only move)> 105.Bd4 Re6 <(The Rook on the 6th line makes the situation of defender worse which is evident from the continuation 105...Ke1 106.Rg2 where the black Rook cannot go on f6 as it is covered by Bishop d4. It is a thing worth to remember.)> 106.Ra2 Rc6 <(This is the same position as after move 101...Rc8 with the only difference that the Rook of weaker side is on the 6th line instead of 8th. But the difference is crucial here.)> 107.Rd2+ Kc1 <(or 107...Ke1 108.Rg2)> 108.Rg2 Kb1 109.Rb2+ Kc1 110.Rb5 <(with deadly threat Be3+)> 110...Kd1 <(if 110...Rd6, then 111.Ra5)> 111.Bc5 <(pretty final nuance)> 111...Kc1 112.Be3+ Kd1 113.Rb1+ Rc1 114.Rxc1 mate.