You are not addressing anyone cognizant from Apple here with the exception of the forum creation staff, forum moderators and a few "official" forum community technical specialists.
Everyone else that responds here are just Apple product users just like you.
I am using the desktop version of YouTube in a web browser and background YouTube playing from the Home screen is working fine.
You can't use the mobile YouTube website OR the YouTube iOS app, if you want to get videos to play on the Home screen or while using other apps.
Also, another workaround was mentioned and explained using the website Listen On Repeat.
This method, while a little more involved, works.
We're all using iPads with iOS 10 and I don't understand why some users, like myself, are having success in getting YouTube videos to play on the Home screen of their iDevices/iPads and others can't get this to work.