It's clear he didn't particularly understand it either. He took the manifesto as a call to make paradise on Earth. His opening statement was saying that paradise cannot exist on earth, because living as a human means existing within brutal, uncaring nature.
He brought up that the manifesto doesn't mention nature like this, which is true, it's a political manifesto for organizing factory workers. If he had read Capital he'd know Marx defines labor as transformation of natural resources through human ingenuity.
I don't think Peterson ever cared about history or theory as much as vibes. I don't think he even regards facts as important. He likes little anecdotes that signal things with metaphorical truths.