I think it's for mounting the Trackball into a metal panel, but Randy would have to confirm that for you because I bought my Trackball elsewhere and then bought the Electric Ice upgrade kit for it. The flat piece, you are talking about, is a spacer plate that Randy supplies with it.
If you don't want to see the mounting plate, then you have to route a recess into the top surface to take the plate, and lay your artwork over the top of that, with a hole big enough to allow the ball and surrounding ring to poke through the artwork and the plexigalss if you are fitting it. If you don't mind seeing the square mounting plate from the mounting kit on the top of your panel then you just bolt the mounting plate to the track ball and drop the whole thing into the hole you cut. Betson is the leading wholesale distributor of commercial arcade game machines from Raw Thrills, LAI Games, and morea full line of games for sale. What you do then, depends on whether you want to see the mounting plate or not.
If you're mounting it in 3/4' wood panel then you need to cut a hole the shape of the entire plastic case for it to sit into. The Electric Ice is actually a 3' Betson Imperial Trackball.