The normal rules of chess still apply so you cannot move into check with your king. But if a player checkmates your king, then that player loses.
Player 1 checkmates player 2--->Player 2 wins
Player 1 checks Player 2--->Player 2 must move out of check.
Player 2 cannot move into check or checkmate regardless. This is the same as in normal chess.
There was never an answer to whether you could move into checkmate, was there?