White to play - draw
In Fine's final line 1.Kg3 Kg5! 2.h3 h6! 3.Kf3 Kf5! 4.g4+ Kg5 5.Kg3 Kf6! 6.h4 Ke5? Black could still hold the draw with 6...Ke6 7.Kf4 Kf6! when White's King is not far enough advanced to take advantage of the extra move h5. 7.Kf3! Kf6 8.Kf4 Ke6 Here, Fine abandons the position as a draw with the comment "White can only win by foul means, for fair ones fail." In fact, White is winning quite fairly with 9.Ke4! Kf6 10.Kd5 and Black is soon outflanked since White still has the move h5 in hand.
Analysis using computer generated endgame tablebase