Unless you really are concerned about a blackout not interrupting your game, there's really no reason to put a UPS on a pinball machine.
A good quality surge protector power strip should be all you need.
Also, make sure you turn the power strip OFF when you're not playing games.
When operated commercially, these games were usually plugged directly into power, and turned off via breakers at the panel box. Hardly the cleanest electrical environment around.
Just imaging what that load center was doing when the guy came in, in the morning, and started flipping all the breakers on, for 100+ games in a large arcade.