But if you assume it's a multi-player game, wouldn't it be easier to implement a global space-time? The reality is that you have to keep an internal clock for each player.
Nothing stops us from arbitrarily designating a particular reference frame as "preferred" in a simulation; SR merely says that such a choice is truly arbitrary. Note also that this system could work recursively, such that new units must always spawn at the spacetime location of older units, and do information management (behind the scenes) in a similar way. This would turn the network into a tree - and the transforms are relatively cheap (and we could use a Spacetime algebra library!)
Note that I don't think this works for a traditional RTS like C&C or Supreme Commander. But rather a game like Civilization, but galaxy spanning (and spanning very long periods of time), where the smallest objects are something like "suns" and "fleets". The individual lives of humans would come and go as these vast battles took place over thousands of years. You'd only need to add magic like a 1g constant acceleration drive - and a strong rule against using this to directly kill planets - and assume that the fleets are actually large-ish asteroids fitted with the drives and a human and/or robotic crew.
The spawn point would then be, fittingly, Sol.
You can transform between two players clocks easily enough. Time is just another coordinate to maintain.
You don't need special relativity for that, all you need is a finite speed of light - a fact which was known before special relativity was developed.
This is from the finite speed of light, not special relativity [1]. Light is very slow, compared to these distances. Heck, it's slow compared to distances in our solar system, taking 8 minutes for the Sun's light to hit us.
[1] https://www.wtamu.edu/~cbaird/sq/2014/10/23/how-does-looking...
Interesting thought. Can you expand? What do you mean by this?
I observe my base and order a group of units to go to some place on the minimap. I see them moving along on their way, and decide to scroll to them. Only to realize that they already arrived and got massacred by the enemy. I go back to my base only to realize that it was destroyed ages ago (in its frame of reference) and I'm dead. Game over. Thanks for playing SR Red Alert.
EDIT: Also if a unit traveled close to C away from a friendly unit, and then back, whos reference is real?
In lore it may be explained like "our units know distances to objects and choose closest one among all units" since we already use "units can communicate instantly" magic.
Also in time I bet some players would find ways to win reliably, creating a new field of military strategy.