I haven't experienced this specifically on YouTube, but you may be talking about the Page Visibility API [0]. I've tried to disable it natively in Firefox and Chrome (without extensions) but with no avail. It can even tell if I switch desktops in i3wm. Here's two demos [1][2]. I'm guessing it's saving $$$ on bandwidth. I just want the option to turn it off.
The pause button make sense, force users to focus on the page briefly every now and then to save bandwidth - Netflix does something similar to prevent long running auto-play.
The looping is quite different though, there's no legitimate use for it, and I can't find any controls that would allow you to set a song to auto-repeat. So it's either a bug that they're struggling to fix or an intentional change to make play-lists less functional when you are not watching the platform.