what's the name of the program/app/daemon that "plays" music in rhythmbox when i try to quit it with close button?

Solution 1:

It's still Rhythmbox, but I suspect that you may have a different version of Rhythmbox on the other distros which is why you see different behavior. There has been some back and forthing over the behavior of Rhythmbox's close button.

But currently, on Ubuntu 12.04, the Rhythmbox close button is simply hiding the player's shell. The player is still running and playing your tracks.