While there might not be many people carrying portable computers now, that is clearly something envisioned by Airfone. The FCC hasn't done that yet, because they want to see the results of our experiment. I'm pretty sure MazeWar does use PUPs. Thus it should be possible to play between say, England, Rochester, and El Segundo, although the response might be a bit sluggish if some players are 4 or 5 hops away. I stand corrected.
Every player simply sends a single pup to every other player in the game on every change-state.
Of course the small number of people allowed in a single maze does help keep the communications overhead down. But the limit was to prevent crowded mazes, not because of communications. The only broadcast msgs are those when someone tries to join a game. Certainly the current version does. There are indeed three windows, but you didn't describe them quite correctly.