As you can see from the screenshots below, the mention of YouTube Red appears when using background play. Android Police also claim that YouTube will re-branding of Red YouTube Music Key, which is similar to Google Play Music on YouTube, and allows the user to view music videos on YouTube without ads, save your video for offline viewing, and play the video in the background.
However, there is another possibility: YouTube Red is an extension of functionality for all YouTube videos. That is, YouTube Red will remove advertisements from all video clips, as well as add them to view offline or background playback.
We can only wait, that Google will clarify the situation at the forthcoming conference in San Francisco.