YouTube Plus (Premium? Paid? Whatever) has Download function. You know, for watching videos offline. Only if you downloaded it, it will continue to stream it from the net. If you go offline (the main reason you downloaded it in the first place!) it’ll just stop playing!
There’s no easy way to switch to downloaded version too. You see that ✓ Downloaded checkmark? If you click on it, YouTube will offer you to delete Downloaded version. You know, because that what you obviosly wanted to do when you realise you don’t have internet and your video stopped playing, right?