Your sentence as written is just fine, as long as you change the plural verb "act" to the singular acts, since "the essential destruction" is one thing and therefore needs a singular verb. The words within the commas function as a kind of afterthought (technical term: non-restrictive clause):
The essential destruction of the human species, and the state of society that follows, acts as a metaphor for the technological desensitization of human society.
Here's a different sentence which illustrates the same sort of thing:
My younger brother, as with the four siblings who followed him, has a magnificent mind. He decided to put his brain to work in medical research.
If you choose to make your sentence one, long sentence without commas, it would read,
The essential destruction of the human species and the state of society that follows act as metaphors for the technological desensitization of human society.
The two phenomena ("the essential destruction" and "the state of society") require a plural verb.