Having looked at the site and video for the game, do you really need CNC?

By the looks of it, you need a grid, which could be as easily made from strips of wood, notched + glued together, 4 sides, and a top & bottom.
All that could be done with a table saw, and a router table (cross cut saw would be far safer/more accurate, but cost more to buy), along with a few jigs, so you can machine parts in batches, then assemble them.