While this is a great deal for Play Music subscribers, I'm not sure if YouTube Music Key's offering is strong enough on its own. There are many free apps for Android and iOS that let you play almost any YouTube video in the background, not just music videos. They also let you download almost any video and don't show YouTube ads. There are various ways to block YouTube ads and download YouTube videos.
I think that YouTube Music Key is a way to improve Google Play Music Key and supplement it with YouTube's music videos. It's also a way to promote Google Play Music's subscription service using YouTube.
Features like playing videos in the background or offline playback should be available for free for any video. Limiting them to music videos and requiring a monthly fee seems shortsighted, considering that there are free apps that offer these features.