You would have a hard time finding a court to enforce your claim too, since the Outer Space Treaty states:

Outer space, including the moon and other celestial bodies, is not subject to national appropriation by claim of sovereignty, by means of use or occupation, or by any other means.

Seriously, depending on how long your game is, it might make sense. You would expect at first the claim would be completely disregarded, and then in some number of centuries enough inter-planetary infrastructure could develop that includes a legal framework under which you could sue for damages. Or, something...

I wonder if you could send over some type of networking equipment, and then anticipate charging one heck of a bandwidth premium?