Mmmm, if your wall-outlet is ungrounded, there's very little use in a grounded step-down.
I grounded everything in my Gameroom, but according to regulations it's not necessary in Holland (because there are earth-leak protectors on ungrounded groups).
Grounding is only required if you're going to run your Ms.Pac in a "wet" area like your kitchen or bathroom
Also, if you insist on grounding the machine you can simply run the ground wire directly to the ground point inside the machine.
O wait I see there's an ungrounded plug on this one. You could replace that with a grounded plug and factory attached 3 core wire and run the ground-wire to ground connection inside the cab.