You know, that's not such a bad idea. The only problem is that people would have to download the movie files. Unless those files would be linked externally, such as by a url, but I am not even sure if OGRE allows for that. Then, the host could just overwrite the file wherever it's uploaded with new movies every time they're streamed.
Another way could be to have the host's screen streamed online to a specific url, which is then linked in the material file, in order to stream the movie on the screen in real time.
However, I am unsure if the OGRE version that the game uses is capable of that. They've had a few updates to the engine after FH came out, so it might not be up to date enough to even manage that. Not to mention that it would add extra load onto the server.