I play music videos on my nvidia shield, the YouTube app does not have the ability to shuffle playlists, but you can cast and shuffle, however, the YouTube app shuffle is terrible. It shuffles the 20ish most recent videos on your playlist. I have tried NewPipe which is nice and can shuffle but still has the same issue as the normal YouTube does. I would prefer to not cast, the YouTube music app actually does shuffle playlists normally, but some videos are unavailable and sometimes I have issues where for some reason the cast stops. If anyone has any recommendations thank you!
YouTube Music