The idea of time-travel games is very interesting. I believe there's at least one time-travel based RTS game.
However, the mechanics of such games are very complex. Also for multi-player games the main limiting factor seems to be that the central time-travel fiction of jumping timelines doesn't really work once you're trying to facilitate multiple players. That's because all players actually exist in this shared external timeline, and trying to justify in a time-travel game why there's this external clock (the real world time) is both complex and heavily limits the "rules" / time-travel "system" you can have in your game world.
So, a multi-player time-travel games requires that all players are effectively godlike entities that actually exist in single external absolute timeframe (the timeframe of the real world). For games that have linear time, this is no problem at all, since time can just go faster or slower in the game depending on what you're trying to depict. But for any sort of "non-linear" time, the fact that we actually exist in real linear time gets in the way. If you have a single player then time travel is no barrier to narrative, since you're effectively Marty McFly jumping back and forth, but with a single linear perspective of time. But if you had, say, someone playing as Marty, and someone playing as Biff, and Biff stays in 1955, Marty suddenly can't hop forward 5 years to see what Biff is doing, since both Biff and Marty actually exist in a sychronized time frame, which is our world.
Yeah, so time-travel game is a great idea. But you can either do a free for all time-travel thing with a single player, or you can do a much more limited type of time travel with multi-player. It's the MMO part that breaks the idea. So, each player could be a "time agent" and time agents exist in "meta-time" or something, which is our world's real time, and they can travel to different places and times and enact events.
Another core problem with time-travel games is one of scope. Games currently have a lot of problem giving meaningful differences when you go "off the rails" even in small ways in their linear narratives. Having a non-linear narrative where you can go back and forward in time would not be practical to create detailed scenarios for. So, you'd have to use procedural generation to generate events / story. The best you're going to do is something like history mode in Dwarf Fortress, but the player can jump around in time and mess things up.