Let's say I play a YouTube music video on an iPad and then try to play another music video on a Nexus 5. YouTube shows this message: "Playback paused because your account is being used in another location". That means I can't play YouTube music videos on multiple mobile devices at the same time. This is strange, especially when you realize that YouTube Music Key is only available in the Android app.
If I sign out, I can play music videos, but YouTube Music Key features are disabled (background playing, offline caching, no more ads). I can also play music videos in Chrome or other mobile browsers, where YouTube Music Key features aren't available.
Google Play Music has a similar limitation: "If you play music on multiple devices at the same time using the same account, playback will be paused so you can choose which device you'd like to use. To help ensure uninterrupted playback, make sure you're listening to music using one device or computer at a time."
Maybe it would be a better idea to enable Music Key on a single device at a time and disable its features when using other devices. This way, you could still use the YouTube app and play music videos just like any other videos.