My bet is there is nothing magical about the transformer.
What you really need to know is its output voltage or voltages.
You need to find a schematic for the game.
Once you find the transformers voltage values you'll be able to come up with an alternative.
The fuse values will help you size the transformer for each voltage
If it needs more than one voltage you can always use multiple transformers.
As long as you are not trying to keep the unit original.
Good luck.