TIP102 and TIP120 are both NPN Darlington Transistors with the same pinout (base, collector, emitter - in that order, from left to right).

TIP102 is rated at 100Volts 8Amps
TIP120 is rated at 60Volts 5Amps

In this case your replacement (TIP102) is a higher rated part both in voltage and current and is in an identical package with identical pinout so it is a superior choice over the orginal.

These days the price difference between TIP102 & TIP120 is almost nil so it makes sense to use the better part. In the olden days the price difference was substantial and that's why manufacturers used the lowest rated part they could get away with especially when they were using 20 or so pieces per machine - the savings would have been substantial.

As for WHEN the transistor actually shorted - please re-read my original post:

"The outhole solenoid driver transistor is very probably shorted. It can happen in a split second and for no particular reason."

Electronics is a funny beast - you don't need to hear a grinding bearing noise for weeks before your gearbox siezes - it just happens, parts blow up and often there is no particular explanation that you can actually pinpoint!