The rules are pretty complex. and there are some gotchas in there. Here's the exclusion list, where I've highlighted the ones that may screw you:
- Different flights, routes, itineraries, inclusions, travel class, or number of passengers, or different number of adults and children.
- Fares for flights operated by other carriers.
- Fares provided by opaque online agencies where carrier and itinerary details are not known until after purchase are excluded from the Online Price Promise.
- Prices quoted and or charged in other currencies.
- Corporate, wholesaler, consolidator, group fares, student fares, or package fares, or fares restricted to members of certain websites or membership programmes.
- Fares published websites that have different URL Country Code Top Level Domain endings.
- Fares that are offered on websites that do not have the capability to confirm the booking and accept payment.
- Fares that are sold by retailers, agencies or persons who are not accredited and authorised distributors of Air New Zealand airfares.
Basically, they won't price match Amex Travel because you can only book through them if you're a membership rewards member. They may or may not match Expedia depending whether it's a travel agent fare (matchable) or consolidator (not matchable). And that nasty rule about different currencies and/or TLDs can screw you too. I'm assuming you're a US resident? Because the price promise only applies to US or UK residents - Australians can only get price matching between Australia and New Zealand, and New Zealanders can get stuffed (no seriously).