plug.dj is the closest to turntable, in that they use embedded youtube/vimeo videos synced between all the users in the room. Completely offloading their biggest cost (media storage/bw) into public video platforms -- genius.

I would honestly recommend jqbx.fm instead if you have a spotify premium account. plug.dj goes through constant ownership changes, prolonged site closures, and suffers from over gamification+monetization. JQBX is a much cleaner experience with much better support for mobile / streaming on different devices that are connected to your Spotify account.