ScreenOut is a handy Chrome extension which makes it easier to watch videos on YouTube, Netflix, Vimeo and more.
If you find a clip you'd like to watch while doing other things, ScreenOut can display it in a floating window which stays on top of everything else (your other applications, too, not just browser windows). There's minimal clutter, so most of the window is available for the video, but you can also resize it to suit your requirements.
Usefully, if you need to close the viewing pane after all, ScreenOut automatically carries on playing the same video, from the same point, in the original tab (assuming it's still open).
There are various ways to launch the pane: keyboard shortcuts, buttons on or next to the video, maybe automatically (on window blur, YouTube only) or by clicking ScreenOut's icon on the address bar.
If the viewing pane doesn't stay on top then you'll probably need to toggle Chrome's "enable-panels" setting, but that's not a problem - the extension's "Options" page has step-by-step instructions, with links, to show you what to do.