Push Fight!

Based on http://www.pushfightgame.com/ . You can buy a wooden version of this (with box and instructions!) here https://store.penny-arcade.com/collections/media/products/push-fight . (note that this benefits me in no way, only the creator and distributor of the game, I'm just a fan)
Instructions on how to play can be found at both links.

I think I added a basic improvement over the available model by allowing the anchor to actually sink into the square piece and the gameboard below.

If