You're right that serious domestic disputes never actually have a 'winner', in that their very existence is an indication of a breakdown in the relationship somewhere to the extent that emotions boiled up to the point of a verbal fight. Even if you win one of those arguments in the traditional sense, both sides still lose because of the breakdown in trust and the hurt experienced by the losing side.

But Crichton seemed to understand that. His essay contains advice not on how to triumphantly win each and every fight as though you were in a high school debate, but rather on how to resolve domestic disputes without them turning into fights, how to limit the emotional damage fights can cause and, importantly, how to do all of that without being weak and merely acquiescing to the demands of your partner no matter what. As such, it's really better described as a guide to domestic dispute resolution.