Def would verify against another IJ or same era xfmr before splicing back together. If everything worked fine w/out that connection I’d be hesitant to remake it unless someone can verify it (or via manual/schematic)... but if you end up remaking the connections don’t just twist them. You want a solid connection - either twist and solder and heat shrink or crimp on electrical connectors after stripping back casingS and make the connections that way.

Kinda looks like a op hack job of converting 110<->220

This type of thing is seen on a lot of games that are exported/re-imported

Those 2 wires are needed when the transformer is operating on 103/206/218 Vac.
So if you have 115 Vac coming from the wall, it is not used in the configuration.
Reconnect and insulate them would be best option.
Pull cord from wall when working on transformer.

FYI: There are a few posts here about the speaker hum. Start by isolating the board from the backplane and see if it goes away. If not, an add-on power supply can be used to power the sound board alone.