Why is "man" used where a plural might be appropriate, and not "men"?

Man is being used as a singular collective term describing all of humanity.

I believe that the point is that "Gods" and "Kings" would be separate entities (or special distinctions) that would be distinguished within mankind or distinct from mankind. The point of the phrase is to say there is only one group, "Man", and no important other distinctions or hierarchies.

A passage from Anthem by Ayn Rand:

At first, man was enslaved by the gods. But he broke their chains. Then he was enslaved by the kings. But he broke their chains. He was enslaved by his birth, by his kin, by his race. But he broke their chains. He declared to all his brothers that a man has rights which neither god nor king nor other men can take away from him, no matter what their number, for his is the right of man, and there is no right on earth above this right. And he stood on the threshold of freedom for which the blood of the centuries behind him had been spilled.

The quote is based on the principle of Objectivism (proposed by Ayn Rand) which focusses on the importance of freedom from all kinds of authority for true happiness. Man is pitted against gods, kings and his fellow men.

It is true that the narrative elements of the game are heavily influenced by Objectivism as @peerless suggests. Arguably, the narrative is a critique of Objectivism, or at least, "It's about what happens when ideals meet reality."

it was hard for people to understand exactly what I meant by "utopia." I didn't mean a place where everyone holds hands. [...] They started building a hospital, and I said, "No no no, it has to be thirty competing businesses, really crass advertisement." [...] There's no central administration. Everything's about competing businesses.

The game is full of "crass advertising" that is often totally unveiled propaganda for the point of view of the particular faction.

Though "man" is often used for "mankind," the singular "man" in this particular case is intentional and reflects a sort of militant Individualism that the underwater utopia was built upon (the Ryan faction).

http://www.shacknews.com/article/48728/ken-levine-on-bioshock-the