If it's to watch a movie, why bother with the capture card at all? Why not throw together a way to stream the video from the Pi doing the text overlay to all the remote participants.

Is the GP commenter suggesting that they'd like to have people in remote locations each load a copy of their DVD into a player at the same time so they can comment on it together? If so, then yeah, you need a capture card I guess, but the notion of doing that seems a bit bonkers.