The mistake was 98.Rh7+, allowing White to penetrate with ...Kg6 (guarding the f-file from Black's King) and subsequently ...Re5+, cutting the Black King well and truly off.

Schlechter appears to be cruising to victory when he too fails to appreciate an unexpected reply by his opponent.

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<28.Nf4?> is refuted by the spectacular <28..Qe4!>. This loses a Knight for three pawns and gives the initiative to Black. Tarrasch needed to calculate this carefully as his King is now exposed, and White has two connected passed pawns on the Queen-side. It is probable that instead of taking the <d> pawn on move 30, Tarrasch would have been better off holding onto his <e> pawn for greater King security.

Schlechter obviously believed that he still had practical chances as he ignored a three-fold repetition on move 38. Tarrasch, however, has the better position.

<38.Rh4> is a straightforward blunder that neither player appreciated at the time, <39.Qb3+> followed by <Rd1> wins Black's Knight.

<54...Qxb2?!> allows Schlechter to obtain K-side initiative with <g4>, <54...Rd5> threatening <Rd2> seems strong.

<57...gxf6?> leads to mate after 58. Qe8+ Kg7 59. Re7+ Kh6 60. Qf8+ Kh5 61. Qf7+ Kh4 62. Re4+ Kg5 63. Qg7+ Kh5 64. Rh4+ Kxh4 65. Qg4 mate)

I think you are right. I've seen it said at one time it was 6 moves though I always thought they meant three moves each so it was still 3 fold rep.

Yes, it is a <theoretical> draw after 80.Kg5. But this game was played between two human players and human players make mistakes (chess engines too, just different mistakes). I went through the game move-by-move starting with 80.Kg5 using the 7-piece Lomonosov tablebases and here is what they indicated:

(a) The game is a theoretical draw from 80.Kg5 through 95.Kh5 assuming best play by both sides.

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(b) Black blundered with 95...Rh7+ after which the tablebases indicates that White theoretically mates in 31 moves. I again have to say "theoretically" because White can make mistakes just like Black can and thus change the theoretical result. But instead of 95...Rh7+, 95...Rf1 is still a theoretical draw.

(c) In the final position after 106.Rg1

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The tablebases indicate that White theoretically mates in 21 moves. The winning sequence is interesting and possibly instructive. Per the tablebases, with best play by both sides, the game could continue (and I say "could" because at any point a different move(s) would allow White to mate in the same number of moves as the "best" move) as follows: 106...Rb3 107.f7 Rf3 108.Kg7 Ke7

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This position suggests a diagram because the winning sequence is "cute": 109.f8Q+ (109.f8R would work as well, but in this case neither 109.f8B+ or 109.f8N. But see https://en.wikipedia.org/wiki/Rook_.... The page says that "Endgame tablebases show that 40.1% of the legal positions with this material are theoretical wins, but that includes many unnatural positions that are unlikely to occur in games. Edmar Mednis estimated that less than 4% of starting positions that occur in games are theoretical wins." I would be interested to know how he estimated that. Sadly he passed away in 2002) 109...Rxf8 110.Rd1+ K(any) 111.Kxf8 and White mates in 15 moves.