I remember one action game on the Apple II that played music during gameplay: Microwave. But the sound was made on purpose to sound kind of choppy (a bit like voice fry), so that there was some leeway to fit graphics updates and calculations. I never disassembled it but I can imagine the pain it must have been to keep the game loop close to constant time.
By Jay Zimmerman and Jim Nitchals. The choppiness was key: it played the note uninterrupted (literally!) for just long enough to let the listener ascertain the pitch, but not so long that it interfered with the rest of the game loop.
I never disassembled it, either, but my teenage ears sensed that the sound was still playing, albeit at a near-inaudible frequency, even during musical pauses. I assumed the game would set a memory location somewhere to indicate the note to play, and the sound routine's job was simply to play that note (probably attempting to keep a constant time as the frequency varies). That kept the frame rate consistent even if there wasn't sound to play.
The Bilestoad would have been utterly incredible if it had embraced the mockingboard. Then again, the slightly labored and off-key fur elise coming out of that sad little speaker while you hacked away at your enemy had a creepy charm.