Put a plywood sheet on the sawhorses. Using the measurements provided, draw the cabinet side onto the plywood.  Take your time with this step.  If you screw this part up, your whole cabinet will be off.  Use the best long edge of the ply as the back and work from there.  The back and base should

FYI- The person you see in these series of pictures is just a prop.  You can safely ignore him. 

To prove the measurements were going to work,  we built a prototype.  We started with a scrap piece of 1/4" ply we just had lying around.  We carefully measured the controller section onto the ply and cut it out with a jig saw that had a fine tooth blade in it.

We propped the X-Arcade controller up on 2x4s so that it was at the height the design called for.  This was done just to ensure it was a height we were going to like.  It was.

You can skip this intermediate step if you trust the supplied measurements to be correct.  They are.