That's a good question :)

I was wondering about this myself, it feels and probably is possible, and I have some ideas on how to do it. Though, on the one hand it would be cool if the entire GB was emulated using compass-and-straightedge, but OTOH, it would be less "pure" and a little more "forced" than just simulating the ALU, if you get what I mean.

One idea I had is trying to draw the graphics of the game using compass-and-straightedge constructions (i.e., using circles and lines to draw approximately the GB graphics)