>>20996010GBA music is in a MIDI-like format. I don't know the details, and I think it varies depending on the individual game's sound engine (getting more than 2 PCM channels requires additional processing by the CPU - that's why technically impressive GBA games always have shit music, fun fact).
That said, they could always just record the original music from the games and stream it. It takes more space, but XY in their entirety were only something like 1.7GB, so clearly they have some serious compression going on.