There is that
this YouPlayer 3rd party YouTube which i mentioned
earlier in this topic which supports PiP and Split View and Slide Over. It works very nice on my iPad mini2 with Slide over and PiP.
I also have various apps that have YouTube videos in their app i think (a Dutch tech app called
Bright) and they also offer PiP when you open a video.
For more apps check out
this other wiki topic with apps that support PiP (and/or Slide over/Split view)
Taking a look at that app, it appears to just embed the youtube videos, which will make it use Apple's player, which supports PiP.
To be clear, Youtube, either the website through Safari or the official app on the appstore do NOT support PiP. Google are always slow on the uptake with updating their apps, if they ever adopt PiP, slide over or split view, it'll be on their app, and not very soon.
I can't see them updating their web player to offer PiP, if they do it, it'll be in the app. If anything, I would argue they have a vested interest in not updating it, like netflix, I'd imagine they want you to stay within the confines of their app. That way they can control what happens when the media ends and offer you up new content, which they can't when the video is in PiP.