I was just saying that Youtube red is their pay service that gives you enhanced features including the background streaming using the actual app. Safari has always allowed the background streaming on the YT mobile site, even before the whole YT red pay service. For me it only works on Safari not Chrome. Now why it doesn't work on your phone is the real question. Their has to be something not allowing it to work.
This used to work just fine for me, but now after locking the screen and pressing play, it tries to play the last song I was listening to in Music, but doesn't actual play. I'm on 10.3.2 beta. Will let you know if the behavior changes in beta 2.