This happens presumably because your Prince of Persia installation was configured to produce audio using the PC speaker, not a sound card. In later versions, the setup tool (
SETUP.EXE) can be used to choose the appropriate sound device:
In earlier versions, the sound device is supposed to be auto-detected, but this can fail, and the default then is the PC speaker. The sound device can be specified as an argument to
In most desktop computers, this would produce sound using a buzzer in the PC case (if it has one!) rather than any loudspeakers or headphones connected to the PC’s audio output.
See Why did the IBM PC need a sound card? for context.
(Some desktop PCs would re-route PC speaker audio through the sound card, but that was apparently not the case in your computer. The majority of laptops use the same audio-producing hardware for both PC speaker and whatever sound card they have, so this doesn’t happen there.)