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Is this game a win for white?

Yes, per FIDE Laws of Chess this is a win for white.
Black does not need to lose the rook, he only needs to promote to a knight and then there exists a series of legal moves that lead to checkmate in the corner.
The other website incorrectly applies the Laws of Chess.
Yeah im pretty sure those situations happen in tourney games too. It should be a win if the opponent times out as long as there is a possible checkmate
This is a win for the White player because there's a possible legal sequence of moves that leads to White player checkmating Black's King.

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