The idea of messing up with time has always been a big fantasy of mankind. There are tons of Sci-Fi stories abusing the concept. As a matter of fact, who among us never had this idea popping up in their mind after some particular event happened "if only I had a time machine". That would certainly prevent some major screw-up, huh? And potentially generate others but well... I bet that there are persons in this world who are crying for finding a time machine right now

So yeah, that game could be the occasion to see what realizing mankind greatest fantasy is like. As for the futuristic gun, the lead designer addressed that in his blog. Futuristic guns will be used in historical periods but only if there's a good reason to do so and only at appropriate times. As a "time agent" the player's actions will necessarily unbalance things so he'll have to re-balance them. As the storyline goes, the player is apparently not supposed to win a battle that was historically "lost" (so for example if he unexpectedly contributes to win for the Russian a battle that was lost during WWI he will have to come back on the German side to restore the "historical balance"). What he'll have to do is to prevent some people involved in these battles from stupidly dying here so they may continue to live and have their little good impact on the future of humanity. The thinking behind this would be: How many people died in a war that could have been the father or mother of a guy that 30 years after would have had the greatest idea a human being ever had, an idea that would have brought peace and happiness to the world? What if the father of Einstein died during a war before he was born? What if the father of Newton or Franklin had been slaughtered on a battlefield?
And what if Britney Spears never climbed down from a car without undies? (Oops, no I'm pushing it too far).
The character's motivation for going through all of this is of course that if he doesn't do it, the bullet (or whatever) who was meant to kill him will kill him. If he does it right, the bullet might miss him or the war he was fighting in never happens. Of course he would have also to take care to not modify too much because chances are that he would never be born.
Anyway, time travel has been exploited in all aspects across generations and generations of Sci-Fi authors and as weird as it may seem there are actually scientists working right now on the concept. Well even if they don't come with anything functional, I assume their research will always give some interesting prospects in other areas.
Although there are many theories about time, the one currently the most widely accepted and derived from Einstein's work is one where time travel cannot be used to change the outcome of events anyway. Roughly put, you could travel in one timeline to be a witness of events but without being able to change them, or you could jump from one timeline to another timeline in which events would be altered (but there again without the possibility for you to change them). Each timeline has its own sequence of events and there is an infinite number of timelines (or universes since that's how Einstein work put it). Infinite because everything that can be imagined happened, is happening or will happen but not everything can happen at the same time in the same place (that would be a downright mess). So according to the theory an infinity of timelines is the way nature would have found to keep things clean. So for example, there is a universe where you are filthy rich, with the lady of your dreams and in the seventh heaven, another universe where you are poor and miserable and another universe where you were never born and of course even a multitude of universes where humanity never saw the light of day in the first place (which suppress a wide range of problems) and even more where Earth never existed. Differences between timelines range from very minor to staggeringly huge. In this vision of things, admitting that you could change an event in the past, the only result for you would be to jump into a different timeline already containing the result of your actions; your own timeline would not be affected. And that would pose the problem of your potential "double".
Of course there is the other theory -- considerably older -- that the game is exploiting in which there is only one timeline that can be changed at leisure (plus additional theories that were developed where yeah, you can change events but the time is elastic and find a way to cancel the effects of the changes made...
et al).
It's always fun to try to construct a story around time. I had a lot of fun with that myself when I was still writing Sci-Fi. For example I had this futuristic society that found a perfect way to have a perfect peaceful world. They didn't remove war from their agenda but each time they had a bit of a fight that would require a full scale engagement, they just made a lottery to chose the needed soldiers among the population, and thanks to a huge mean of time travel they invented sent them back in time with all their equipment to fight in an unoccupied territory of the past world generally late at night to reduce the chances to be seen. The engagement would last the whole night and before dawn everything was sent back to the original time period where a winner was declared following the recorded performances. That way, the peaceful world could keep its world... well, perfectly peaceful with no war actually happening in real time that could have threaten the society itself (war kinda became a sport if you will, but the kind of sport that no one really wanted to witness). Unfortunately, one night a screw up occurred and a guy from the past found himself involved in one these battles with consequences... too long to describe here.
Anyway, always fun... Except when you start to think too hard about what time is... It can quickly become a real headache.
A lesson to keep is that in its infinite kindness Mother Nature decided to not let human know what they miss by choosing to turn left instead of right at one point of their life and what they could have achieved if they took another decision. Yeah one can imagine what it would have been, but one can never be sure. And that ignorance is a true gift, otherwise most people -- myself included -- would probably find more than one reason to kick their own ass. That ignorance allows us to keep the lessons, to have no regrets and to pursue the course of our lives like if we never ever screwed anything even if we did.
OK, I'm becoming a little bit too philosophical today so let's get back to the topic:
This game could be a lot of fun.