The full set of constraints (monopoly, durability, constant MC, timelessness) can hardly ever be fulfilled. So it is not falsifiable by empirical data.
But nobody has questioned the logic conjecture itself here, even the article doesn't try. It seems pretty plausible, doesn't it?
An equilibrium for a given game is - depending on the equilibrium concept (bummer, even more conditions) - is a stable outcome of some sort with usually no claims as to how it would actually be reached.
By that, you can already see that this is not really an actual theory of an empiric situation, but rather a mathematical model of a certain solution structure.
If you were to write this paper today as an economist and your goal was to claim that is actually, really holds in reality, then you'd not only have to produce the theory but you'd also have to build some sort of empirical model that you can estimate with somewhat plausible identification conditions and structure, or be able to show it in a (pseudo-)experiment setup that is believable enough. Suffice to say that there are very few such claims made on reality in modern microeconomics (that is to say, Game Theory by and large)
As it turns out, these sort of mathematical models have quite a bit of value in a normative setup, say if you go and design a market or an auction. Less so as a theory to explain all of reality.
I think in Coase's time, it was easier to write a 6 page paper from your bathtub and claim something about the world. Wasn't there an xkcd comic like this?