Are you sure this is a OneWorld ticket? What does the "Fare Basis" say? It really shouldn't be in M. If it's going through a consolidator then it almost certainly isn't a OneWorld ticket since those are fixed price and no reason for a consolidator to get involved.

That being so, the rules of the OneWorld tickets are irrelevant - you need to know what the rules are of whatever it is you have bought.

As far as I can see, only Air New Zealand flies AKL-HNL. If you're flying that route direct then this definitely isn't a OnWorld ticket since ANZ are Star Alliance!