Sorry to tell you, but that is streaming :)
The more I think about it, my idea of "streaming" involves allowing 10,000+ people to "stream" videos from the same server at the same time (everyone watching different videos). I'm pretty sure you can't do this with a normal http server like Apache, because you'd run out of available connections.
My nod toward Twiggy reflects the idea that video would be streamed to all clients in chunks, depending on "where" each client is in their stream.
I know that you have set limits on the number of open filehandles and whatnot, but that's another problem which may have its own solution.