I didn't say he was. I did link to a postmodernist who claims a Marxist approach. There's no pope of Marxism to decide who is and who isn't a marxist. (Though in the case of Trotsky and others, Stalin did want do decide such things, but I don't think we have the modern day equivalent of Stalin around.)
You point to a couple of fiction writers as a high point of postmodern thought. A 'cultural logic' of a meaningless life isn't exactly an uplifting approach.
And, I doubt that anybody has written down the postulates of that cultural logic. Which means it isn't a logic, but merely a pose.
I suppose you can come up with a scenario where logic doesn't mean what it did to Isaac Newton. But then I'd just note that you are playing word games that must generate meaninglessness because there is no assigned meaning to anything. And you'd disagree, and I think we'd have to leave it at that.
Word games is what the postmodernists say everyone is doing anyway. But the esential idea of PoMo is that the relationship between symbols and what they refer to had become unglued over the centuries and even if the relationship seemed strong it was just a rhetorical shellgame. It was a useful idea to a degree and accurately describes a great deal of our culture in a disconnected, media saturated age.