First off, in NZ it's called "GST" (Goods and Services Tax), which is similar to what the US calls "Sales Tax" and what other countries call "VAT".
Apple indeed would not pay any GST here because Apple is not the final retailer*. The final retailer would collect the GST from the sales of Apple goods and pay it directly to the IRD. Wholesale sales of the goods from Apple to the end retailer are GST exempt provided that they are sold to a GST registered business for the purpose of resale would would account for pretty much *all* of Apple's sales in NZ.
* As far as I'm aware there are no "Apple stores" in NZ, all of Apple's products are sold through other 3rd-party retailers here. Even if there were an Apple store it likely would not be directly owned by the same Apple NZ corporation that this article references.