"Larger mountain chain" could refer to various parameterisations, but Mont Blanc's peak is just over 4,800 metres above sea level while Aoraki's peak is just over 3,700 metres above sea level. Given the Earth's equatorial bulge and the difference in the two mountains' absolute latitudes, it is possible that Aoraki's peak is farther from the centre of the Earth than Mont Blanc's peak.
Since for many islanders and coastal peoples the sea is more important than the land (as documented by
Epeli Hau'ofa amongst many other island studies authors), the UK claims a far larger EEZ than NZ
http://www.cpahq.org/cpahq/cpadocs/UKNDA%20EEZ%20and%20Territorial%20Seas.pdf although the UK numbers appear to include the UK Overseas Territories whilst the NZ numbers do not appear to include NZ's "self-administering" or "self-governing in free association" territories.
In summary, these metrics are more for games than for being useful and, irrespective, NZ, Shetland, and Svalbard amongst many others deserve their rightful places on maps. Does this preclude boxes? It depends on the purpose of the map, such as the balance between using the land, the water, and the areas in between. Because some people do want, use, and need maps which are mostly open sea.
Ilan
Twitter/Instagram @IlanKelman