There is no auto-claim because the 50-move rule is not automatic. You must manually claim it at an appropriate time by pressing the draw button (for your game, anytime after white's move 124 and before black made a capture on move 140).
Similar is true for the threefold repetition rule - it is not automatic and must be claimed by a player at the appropriate time.
https://www.chess.com/live/game/2085704784
last pawn caputered at move 74. Still 69 moves possible... till 143
why is there no auto claim?