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g2 is defended by black's knight, so after Kxg2, black captures the king and wins with Nxg2.

Yes but there is no check. So why can’t you move your king into check? You are not moving him into checkmate, after all

You can move your king into check, so white’s move of king takes queen is legal. But, it still is losing because black then plays knight takes king.

Thanks I missed the rule where game ends by king capture, not checkmate