I listen to YouTube music videos on my Android smartphone all the time, but it is a "first world problem" that YouTube stops playing when you turn off the screen of your phone.
I searched around the web for a solution that would fit my needs, but I couldn't find it. All involved rooting my phone or installing apk's from the deep web... Or, alternatively, pay a monthly subscription. None of which I liked...
So I developed Black Screen of Life, which allows you to turn off the screen of your phone while you listen to music videos. It does not require root and it's available on Google Play Store. It greatly increases your battery life! ;)
If you are interested about it, just Google Black Screen of Life! You won't be disappointed!
PS: #nodesignerhere, so the app is a little derpy :P