It wouldn't be illegal to save it for your own private non-commercial use.
You can bet that uploader simply took it from somewhere else and is earning something from youtube as compilations like that get a lot of views
Both Chrome and Firefox offer extensions which can download video from youtube or similar sites.
You could then edt out a short section you wanted with most video editor software.
It might be easier to screen record while playing the clip - again screen recorders are widely available for computers and mobile devices.
You could even use another camera or phone to get a passable copy literally filming the screen on best resolution.