From your story and provided link, it appears that there is no firearms ownership in Norway. That one must rent a firearm from a approved dealer.
Svalbard is under a treaty from 1920, which has Norway administering the Svalbard Archipelago, with guaranteed rights of access to Denmark, France, Italy, Japan, the Netherlands, Norway, the UK (includes Australia, Canada, New Zealand, South Africa, India) and the United States.
Svalbard follows Norwegian law for firearms permits otherwise.