I like this idea, but can't explore it as I don't have anyone here to play it with.
Would be a great candidate for a random multiplayer matchup game. I know it would be tricky in the strict time limits of a jam, but a single player AI opponent would also work well.
As it is, I can only play it 'against' myself. It feels a little bit like the old game Nim, where you have to try to avoid taking the last sheep (or peg or whatever). But I'm not sure because I haven't really 'played' it.
Minor bug: I clicked very near the edge of one square, and it registered the click in the square below it. Maybe the colliders aren't quite aligned properly?