Specifically, I think this is nonsensical:
"Second, it must be noted that argumentation does not consist of free-floating propositions but is a form of action requiring the employment of scarce means; and that the means which a person demonstrates as preferring by engaging in propositional exchanges are those of private property."
It is a well accepted rule in logic and debate that propositions have merit on their own, therefore the way they are stated is irrelevant, whether they consume scarce means or not.
The jump from scarce means to private property is laughable.
Actually I have a hard time charitably following his reasoning. It is obvious the conclusion he wants to reach, but it is hard to understand where he sees an unfolding of logic arguments.
Even if his claims were true, which are, if I understand correctly, that the mere fact of engaging in a moralistic discussion presupposes the speakers assume a kind of private property instinctively, it does not follow that this presupposition is correct.
That's a naturalistic fallacy. It can be used to justify domination, sharing, violence, death of the weak. Using it to defend something as obviously artificial as private property is news to me, and I think pretty hard to defend, but even if it did, it presupposes we should care about "natural law", something most philosophers learned to dismiss since the 19th century.