Carl Sagan wrote a design doc for a video game based on his work
gamasutra.com
gamasutra.com
https://github.com/blevinstein/SRAsteroids
To see what it looks like, you can check out this youtube video:
https://www.youtube.com/watch?v=_hSCz7tRl1s
I wrote an engine that modeled object positions as "timelines", where position varies with time, and demonstrated the basic relativistic effects (length contraction, time dilation, and frequency shifting).
Unfortunately, I never really figured out how to turn these into actual game mechanics.