In this game, the king is a normal piece, like every other piece, i.e., rules on check, mate and stalemate do not apply.
The player that has no pawns left in the game is the loser. Promoting a pawn also results in the loss of that pawn. So, a player wins when he takes the last pawn of his opponent, or when his opponent moves his last pawn to the last rank.
Pawns always promote to kings. Stalemate is a draw.