This claim is wrong for two reasons.
The usual money pump argument deals only with the difficulty of making a choice when your preferences are cyclic. The VM axioms have nothing to do with it.
Even in the presence of cyclic choices, there could be a maximal element among the convex combinations of the choices, see Peter Fishburn on SSB Utility, or Skew Symmetric Bilinear Utility.
I read the article, also. The description of the game was a bit short and somewhat ambiguous.
The game is designed to show people who participate why it is hard to maintain collusion or price fixing amongst oligopolies, secret agreements are not enough. It was a good demonstration of the difficulties in maintaining a secret deal. Far better than simply reading about it.
A number of theorists think that price fixing is mystery because the economics of it should make any agreements disappear.
However, there are price fixings in the real world which are regularly prosecuted. So, how are the Ashley’s dealt with by those groups?