How bout get over it dude, it's a video game, one that is in no way meant to be realistic at all. It's like your logic is "ya I accept that we can now occupy any planet in the entire solar system and one random guy somehow made it all possible and all these alien guys are flying around fighting with each other and these weird robot things can travel through time but we can somehow kill them anyways, that all makes sense but OMG THE GUN DESIGN IS SO UNREALISTIC"
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If something is traveling through time, but is incapable of occupying more than space at a time, then how could you NOT kill it? The time-travel aspect has no bearing on whether or not it's alive.