It's funny, the videos continuing to play when the screen is off, is actually a non-feature for me most of the time because it makes using the back button to get away from a video link you clicked on impossible, you end up having to click back 2-3x and then still hit the x on the little embedded video. The music is already a separate app, they should allow you to disable the background play in the normal app and have it enabled on the music app. Which maybe they do now that I think about it, but I believe when I had checked previously it was a universal setting tied to your google account, not the apps.