The sibling comment proposed a possible scoring mechanism which might result in enjoyable gameplay, but I think the bigger point (for me, at least) is the Mind Chess represents a reducto ad absurdum of the strategy game genre. It eschews as many rules as possible, leaving you only with the goal of knowing your opponent's mind. So Mind Chess is more of a thought exercise.
It's similar to the 2-minute version of Diplomacy - get everyone together and the second sneakiest bastard wins; because nobody will let the sneakiest bastard win.
The Search for the Longest Infinite Chess Game
https://youtu.be/b-Bb_TyhC1A