Your transformer could have a shorted winding, which is causing it to pull a ton of current...which causes the fuse or breaker to blow / trip.

If you dont have a solid background in electrical theory or electronics, this might be a hard one for you. DON'T keep plugging it in to the wall socket. Find someone with a variac or experience testing circuits.

If this were mine, I would disconnect the transformer primary [where AC wall connects] and supply a lower AC voltage with a variac and start measuring AC output. Or reverse feed the transformer secondaries with low voltages and see how things measure.

I'd Nerd out and use my impedance bridge too.

Check your hot, neutral and ground from your power cord and make sure someone didn't tie something together incorrectly. Easy stuff first.

I agree. However, I have had a transformer with an open winding and another with a shorted winding. Both on the secondary side. Not pinball transformers. It happens.

Sounds crazy, but did you check your plug on the cord (where you plug it into the wall) to make sure it is wired correctly. I am assuming it has a 'screw on plug' and not a molded plastic plug.

If you ohm or meter a transformer, you are going to measure low resistances because it merely is a coil of wire from one side to the other (hot to neutral). Yes, there will be separation between the primary input and secondary output. You need to find a variac or impedance bridge to test this properly.

I don't know export games (outside the USA), but that might be a filter someone added and not Bally. Others can confirm. Those line filters were / are used on solid state games. Inside are resistors and capacitors that can go bad.

You can order replacements from Farnell or DigiKey. Those are European suppliers. You just need to spec your AC voltage and current of the game. A 3 to 5 Amp filter would be plenty.