The fallacy here is that HAL lied to win the game. In fact, the game was won in a forced checkmate no matter how many moves it took after Poole played 'Uh-hrumph. ... anyways, Queen takes Pawn'¹. Note here that Poole doesn't observe contemporary descriptive notation for his moves against HAL and HAL's subsequent description of the force mate was either a verbal courtesy for Poole's benefit or a vernacular that the two had fallen into.
Immediately prior to 'Bishop takes Knight's Pawn'
The following interview with the the Earth-based reporter Amor was conducted before the chess game.
AMOR: The sixth member of the Discovery crew was not concerned about the problems of hibernation for he was the latest result in machine intelligence: the H.A.L. nine-thousand computer which can reproduce - though some experts still prefer to use the word "mimic" - most of the activities of the human brain and with incalculably greater speed and reliability. We next spoke with the H.A.L nine-thousand computer whom we learned one addresses as Hal. Good afternoon, Hal. How's everything going?
HAL: Good afternoon, Mr. Amor. Everything is going extremely well.
AMOR: Hal, you have an enormous responsibility on this mission. In many ways perhaps the greatest responsibility of any single mission element. You are the brain and central nervous system of the ship and your responsibilities include watching over the men in hibernation. Does this ever cause you any lack of confidence?
HAL: Let me put it this way, Mr. Amor. The nine-thousand series is the most reliable computer ever made. No nine-thousand computer has ever made a mistake or distorted information. We are all, by any practical definition of the words, foolproof and incapable of error.
Forced mate was the ultimate decision for the game after Poole's Queen takes Pawn'. It doesn't matter whether it wa 2, 4, 6 or a hundred moves ahead of current play. If I was in a forced mate position with stalling moves, I would abandon my stalling efforts and accept the inevitable.
HAL's only 'mistake' was to call his/her moves from Poole's position. That is to say that the black chess board chess move positions were called relative to the the White chess pieces ; they should have been called from black's position. Of course, that could be also be called a courtesy.
¹ The game was in fact a classical chess match familiar to chess aficionados.