Good question. They implicitly assume a dynamic choice principle and a choice function that leaves the agent non-opportunistic.
Their dynamic choice principle is something like myopia: the agent only looks at their node’s immediate successors and, if a successor is yet another choice node, the agent represents it as some ‘default’ prospect.
Their choice rule is something like this: the agent assigns some natural ‘default’ prospect and deviates from it iff it prefers some other prospect. (So if some prospect is incomparable to the default, it’s never chosen.)
These aren’t the only approaches an agent can employ, and that’s where it fails. It’s wrong to conclude that “non-dominated strategy implies utility maximization” since we know from section 2 that we can achieve non-domination without completeness—by using a different dynamic choice principle and choice function.
Just for reference: this isn’t a standard term of art; I made it up. Though I do think it’s fitting.