If this guy bought a gun in New Zealand legally then NZ's gun laws are even laxer than the US's in this case since it's almost impossible for a foreign national to legally buy a gun in the US. Green card holders/permanent residents can but it doesn't sound like this guy had the New Zealand equivalent, he was just an Australian visiting NZ.
"If you are a citizen or permanent resident of Australia you don't need to apply for a visa to live and work in New Zealand. You can be granted a visa on arrival at the border."
https://www.newzealandnow.govt.nz/why-choose-nz/compare-new-zealand/australiaThe same thing goes for EU citizens living in another EU country, i.e. you are to be treated equally as a citizen, which also applies for gun licenses.