I like to think that Games aren't that different from other media. Typically, in most storytelling, the idea is that an audience will always be able to swallow a singular fantastic element (and anything that derives naturally from that element) but not two.
So I think the question really isn't realism per se, but if we buy the singular fantastic element of the Fallout Universe (an alternate "sci-fi" future based on 50s pop culture where people fled to giant vaults to survive a nuclear holocost) is the fatman something that naturally derives from that fantastic element?
Due to the Alien Scares of the 50s, the Alien Blaster seems to fit naturally. The Fatman has a real world historical precedent like the Alien Scares, but given the nature of the universe and its relation with nuclear weapons, the introduction of it as a weapon (and a not rare one) seems to some people to be a second fantastic element and thus setting breaking; others however think that the fatman is in keeping with a logical progression in the settings technological base.
So to me the debate is more "does the fatman's existence require us to suspend disbelief a second time or not" as opposed to realism, since, as you point out, its a game.