Unplug at the wall.
As a first step, I would check that all the fuses in the game have the correct rating, including this one. Watch out for slow blow versus fast blow fuses.
It really should be a last resort for this one to fail
After you have checked them all, replace as necessary - turn the game on. See which fuse blows now. If this one blows again, it suggests the problem is the switch side of the transformer, or the transformer itself - cracked insulation, melted transformer, short somewhere.
If another fuse blows this time, that should narrow down the location of the fault
If you are lucky it will be the contents of that box you have photographed. The silver box with the terminals is called a line filter. Andy at mania sells these. My funhouse must have had a similar little explosion before I bought it. I replaced the line filter, no problems since
What game is it ?