The first time Loche plays chess against the computer he is checkmated by a move which can't be checkmate. Though you can't see the whole board, the place where the enemy queen moves to does not threaten Locke's king, and it moves from a position that cannot reveal any other enemy pieces to threaten Locke's king. therefore it isn't checkmate.

The second time when Locke wins, the whole board is visible, and the "checkmate" Locke receives is far from checkmate. There are two moves the computer can do to escape from check.

Also note that different cuts show different chessboards, and that Locke's first move in the second game is extremely illogical, followed by an extremely illogical move by the computer.

In short whoever wrote that portion had next to ZERO knowledge of how to play chess.