It was public knowledge. Further, there is no such thing as New Zealand territory (or anyone's territory for that matter) in Antarctica. There are existing territorial claims, but they are overlapping and basically nullified by the Antarctic Treaty.
This predates the New Zealand Nuclear Free Zone created in 1984 and in any case this is not New Zealand territory. But land-based nuclear power is perfectly legal in New Zealand, just unpopular & undeveloped, in favour of oil, gas, hydroelectric, and more recently wind. One unusual barrier to NZ nuclear power is that the common designs would be too big to maintain a balanced grid; a single 1GW commercial reactor could supply 1/7 of NZ's electricity.
While legally allowed it would be politically and culturally impossible at this point to build a nuclear power plant in NZ. The population has a strong Nuclear Free identity. For example, when you fly into Wellington, the sign on the way out of the airport says "Welcome to Wellington, Capital of Nuclear Free New Zealand".
It is not really recognized as NZ territory as Antarctic claims are not recognized by most nations.
I didn't downvote you but it takes about 30 seconds to discover that the New Zealand Nuclear Free Zone, Disarmament, and Arms Control Act was passed in 1987, well after the reactor discussed in the article was decommissioned.