I don't think there are any restrictions since as far as I know, the town's website just links to local realtors, anyone that is qualified to buy property there

I don't think there are any restrictions since as far as I know, the town's website just links to local realtors, anyone that is qualified to buy property there can buy property, no need to sign up for a job in the town. It looks fairly easy to get a NZ work visa if you're in a high-demand occupation, but I don't know what the Visa requirements are for a remote worker, so you'd need to investigate that. But there are thousands of small towns just like it across the world, so it's not clear why you'd pick this particular one based only on this plea from the town for more local workers. If cost of living is important to you and you're ok in a country where English is not the native language, you can certainly find areas with much lower cost of living (while still having good internet access)