[prawn]

(Have barely played chess since I was a kid, but guessing below until you get a better/accurate answer.)

White was in trouble before throwing away the bishop as the black queen was in a deadly position, so it looked to get any free pieces it had blocked from moving as a viable strategy at aiming for a draw.

As for the stalemate, I assume the 50-move rule, part (a)? It was either going to draw through losing the rook or via 50 moves without losing/taking a piece.

"The game is drawn, upon a correct claim by the player having the move, if (a) he writes on his scoresheet, and declares to the arbiter his intention to make a move which shall result in the last 50 moves having been made by each player without the movement of any pawn and without the capture of any piece, or [snipped]"

https://en.wikipedia.org/wiki/Fifty-move_rule

[agarden]

No, three-fold repetition would happen long before fifty moves transpired. That's the normal conclusion of perpetual check.

https://en.wikipedia.org/wiki/Perpetual_check