A Relatively Hard Game
Flight simulators with relativistic effects already exist, but Frank is proposing a multiplayer game with relativity. You won't find that kind of game anywhere, and with good reason: it can't be made.
Probably the most oft-quoted attribute of special relativity is "Nothing can go faster than light." More accurately, information cannot travel faster than the speed of light. In a multiplayer game, there's no way to guarantee that players won't talk to each other in the "real world," and that would constitute information traveling faster than the speed of light in the game world, because players could use real world knowledge to make in game decisions.
Imagine the following scenario:
Three players are playing a recreation of the famous battle in which the Battlestar Galactica and the Enterprise team up against the Death Star (shown above, not to scale) using the Space Battle Simulator 2000.
All three players' ships are in a line: Battlestar, Death Star, Enterprise. From the Death Star's perspective, the Battlestar is approaching at close to the speed of light and the Enterprise is receding at the same rate. (The Battlestar and the Enterprise are not moving relative to each other.)
Darth Vader waits until the Battlestar is 1 light-minute away, and the Enterprise is 59 light-seconds away. At this moment, he activates the super laser, which has been redirected through a beam splitter and shoots at both ships simultaneously.
The Battlestar is 60 light seconds away and the Enterprise is 59 light seconds away. However the Battlestar is closing as nearly the speed of light and the Enterprise is receding at the same speed. The Battlestar will be destroyed well before the Enterprise. At least, that's how it works out in Darth's frame of reference if the laws of relativity are obeyed.
Let's say when Commander Adama hears Darth's computer make "Beew! Beew!" laser sounds, he gets out of his chair and walks across the computer lab to see what Darth is up to. By the time he gets there, his ship has already flown into the oncoming beam and has been blown to smithereens. "You sank my Battlestar!" he exclaims.
Captain Kirk immediately banks Starboard, just in time to dodge the laser beam with his name on it.
But consider what happens from Kirk and Adama's perspective. When they hear Darth firing from across the lab, they agree that the Enterprise is closer to the Death Star. But from their perspective, they are motionless. The laser (being composed of light) moves at the same velocity relative to both of them, and reaches the nearer vessel first. According to Kirk and Adama's computer simulation, the Enterprise is destroyed first.
According to the laws of relativity, Adama and Kirk's computers calculate a different chronology of events from Darth's. In the real world, the unbreakable speed of light prevents different observers from coordinating their versions in real time and creating temporal paradoxes like this.