I am not familiar with this system, but I would probably check the line cord box first (game unplugged). See if a wire nut fell off and is touching the earth grounded box or something like that. Usually pinballs have a line fuse that would open before your circuit breaker, that is why I'd probably start in the line cord box.

Something shorted inside metal box over on/off switch ?

LTG : )

Agreeing with previous comments. The cord itself may have an internal intermittent short. I would focus efforts on inspecting and testing everything between the plug end of the cord and the machine's main transformer.

Has anything else been added to that circuit? How much else is on that circuit? If it's at it's limit, just a little extra something could trip it. Also c/b's do wear out, could need replacement.

If the ground had anything to do with this problem, tightening/loosening the connection to the machine would make no difference assuming there's still a ground connection at the wall outlet.

The ground in a three-wire cord is only there for personal safety in case something goes wrong. Any piece of equipment (otherwise properly wired) does not depend on the third wire (earth ground) to operate; only the hot(s) and neutral.

It sounds like the hot wire in your cord/plug was internally touching the neutral or ground. This damage can happen if the cord gets pinched, smashed, etc., or something went wrong inside the plug itself.