Lordvader, I believe what you're talking about it's just a signal transmitter.
To take the example you gave, a signal transmitter grabs a channel for example, and transmits the image through air, pretty much like the old TV antena. You just preset a channel on the device, and all the TV's around certain range of the transmitter will pick it up when they're tunned in that specific channel.
In either way, even if that device you mention does exists, wich I honestly don't know, it would transmit or broadcast a signal of the split screen since it is already coming like that out of the xbox.
Correct me if I'm wrong.