dave-in-nj:
the speed of response is the key.
That's probably why all commercial systems are wire-based, except for the one that's highly secretive on their wireless communication.
It's the real time aspect of it that's not compatible with (most) wireless communication.
Even when using timestamps (which by themselves can easily go in the millisecond precision) you have the problem of precisely synchronising (on a millisecond level) the two player modules.