This doesn't necessarily show that humans have bounded utility, just that the heuristics we use to estimate our utility break down in some circumstances.

I don't see where heuristics came into play in the OP. Heuristics are generally about approximation, and in this case the math is broken even before you start trying to approximate it.

Does one consider the fact that people have non-transitive preferences for certain bets indicate that they don't have utility functions? If not, how is that argument different from this one?

I can imagine fixing humans so they don't have the non-transitive preferences for finite bets. Roughly speaking, making them into a utility-maximizer would fix that. The scenario described in the OP breaks a rational utility-maximizer with unbounded utility and a reasonable prior, so far as I can tell, so it's different.