The Netflix app on the Xbox 360 used to do this. And you and your friends could put on your headsets and watch the same thing on Netflix while chatting.
IIRC Microsoft maintained this functionality however and not Netflix, which is probably why it was eventually discontinued and as far as I can tell Netflix has expressed no interest in making their own similar feature.
The kicker to the game was, 100 other randomly selected players were playing against you answering the same questions. If they got it wrong, and the contestant got it right they were eliminated and the contestant continued.
The goal of the main contestant was to outlast the 100 players, and the more they outlasted the better prizes (usually MS Points) they won. The goal of the 100 was to outlast the main contestant to also win prizes (usually less than the main).
All other players watching the game could participate for fun and play along for no reward. It was actually pretty fun and the events all happened live with an announcer and everything.
I never quite understood why Netflix removed it.