I think I figured it out, and it was fairly obvious. Feeling a bit stupid actually.
The new Asus volume setting lets you choose if a press on the volume button will raise/lower the volume for all sound or for specific sound objects by checking/unchecking the boxes in the sound and vibration setting menu. It also allows you to set limits for different sound objects. For example you can set a 50 percent limit on ringtone and no limit on media. If you crank up the volume to max when playing music, the ringtone will still only be at 50 percent.
So to answer my own initial question, if you uncheck the box for ringtone you can raise/lower the volume for media without turning on sound for ringtone or notifications (there's a specific box for notifications but it seems that if you uncheck the box for ringtone the sound for notifications will be turned of as well, if ringtone is set to silent).
For me this doesn't really add a function I felt was needed. Maybe it can be useful for others though.
Ps. The language on my phone isn't English, so the terminology above might not be exactly what it is shown on devices with the language set to English.
