Doze mode and foreground service
Checking my app's behavior on M Preview device, it seems that its foreground (with active notification) service playing music is not affected by Doze mode. But reading docs it seems that foreground services are exempt only from AppStandby.
What is the real rule?
In this post's comments on Sep 17 Dianne Hackborn writes:
Apps that have been running foreground services (with the associated notification) are not restricted by doze.
So yes, your findings seem to be the intended behavior.