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According to the Lomonosov tablebases,

The position after ​ 58. Kxg7 ​ is a draw. ​ ​ ​ and
The draw remained until after moving to a 6-piece ending.

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According to the 6-piece tablebases:

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61. ... Kg3 ​ loses; Qh4+ was the only drawing move. (If Kg7 then Qxh3.)

62. Qf5 ​ just draws; g5 was the only winning move.

63. ... Qd8 ​ loses; Qxh3 was the only drawing move. ​ ​ ​ ​ ​ ​ ​ ​ (The mates after ​ Qd8 / Qh8 ​ are in 52, but in either case, black deviating from ​ ​ ​ 64. g5 Qg8+ ​ 65. Kh6 Qh8+ ​ 66. Qh7 Qe5 ​ 67. Qd7 Qh8+ ​ 68. Kg6 Qg8+ ​ 69. Qg7 Qa8 ​ 70. Qf6 Kxh3 ​ ​ ​ would speed the mate up by at least 2 moves, so the 50-move rule doesn't save black.)

64. g5 ​ (played) was the only winning move.

70. Kg7 ​ just draws; Kh7 was the only winning move. ​ ​ ​ ​ Since Kh7 lets black repeat, ​ 69. Kh8 ​ made no progress.

70. ... Qb7+ ​ loses; Kg4! was the only drawing move.

71. Qf7? ​ just draws; Qe7 (immediately dropping the queen) is the only other move that does _not_ win. ​ ​ ​ ​ Kh6 was unique-best.

71. ... Qb2+ ​ loses; Qe4 was the only drawing move.

73. Kh7 ​ (played) was the only winning move.

74. Kg7 ​ just draws; Qf4 was unique-best among the four winning moves.

74. ... Qc3+ ​ loses. ​ ​ ​ ​ Qe4 was the only drawing move, but Qb2+ would've repeated the position from 6 ply ago.

86. Kg8 ​ was the unique-worst of the moves that still win; Qf6+ was unique-best. ​ ​ ​ ​ (36 vs 18)

87. ... Qc7 ​ (played) repeats the position from 4 ply ago, which probably makes it black's best try, even though it gets mated in only 18. ​ ​ ​ ​ Qh4+ is black's unique theoretical-optimum, and gets mated in 34.

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I was quite surprised by (the missed) ​ 70. ... Kg4 ​ being an only-drawing-move. ​ ​ ​ ​ A very brief search of nearby positions suggests the "explanation" is it clears the h-file for checks from h1, while taking g5 and f5 from white's queen.