All you have to do, at least temporarily, is run a wire from the exposed metal on both machines that cause the shock. Problem will be solved. Of course, if one machine is not really grounded AND there is a short between a positive circuit and the bare metal on that game's cabinet, connecting ground to that game's bare metal will blow a fuse and could damage the circuitry that is making contact with the ground braided parts.

It still will cure your shock issue.

If I read this wrong and you get zapped when touching the cabinet and you are just touching the floor, run a ground wire from a verified grounded outlet or copper cold water pipe (nobody has steel water pipes in their homes anymore, do they?) to the exposed metal on the pin cabinet to cure.