A chess term for one who only knows how the pieces move. They do not know any strategy behind these moves.
Relevance: Back in the day, chess pieces were made of wood. To be called a wood-pusher is an insult. It means you know only how the pieces move, and no strategy towards the game of chess at all.
Person 1: Dude, do you really want to play me at chess?
Person 2: Yeah I'm really good!
(Person 1 defeats Person 2 easily, without even having to think.)
Person 1: Man, despite all that yang talk, you're just another wood-pusher.