In real life, Joe actually recognized the similarity to Newcomb's problem, realizing for the first time that he must become timeless decision agent, and noting his 90% certainty, he self-modified by adopting a moral pre-commitment to never leaving Kate should they marry, proposed to her sincerely, and the rest is history.

It would be a (probabilistic approximation of a) Newcomb problem when considered without the ability to precommit or otherwise sabotage the future payoff for one of your future options. Having that option available makes the problem one that would be solved correctly by the same causal decision theorist that would two-box.

If you hadn't mentioned the whole moral precommitment possibility (and implied it wasn't available) then I would agree that Joe faced a Newcomblike situation. As it stands it is an interesting game theoretic situation involving an agent who can predict the decision you are in the process of making.

Fortunately humans come with a moral system capable of full sincerity at one moment and then inevitable update in the direction of self interest as necessary. Rather like 'compartmentalization'.