Population density is one thing. Another issue is timing.

New Zealand was a really young country when railway technology came along, and didn't really have enough time or money to invest in a good railway network before other technology came along.

Airplanes are the perfect technology for NZ's geography, because they just fly over everything. There are actually a few places in NZ that received passenger airline service in the 30s before they received a railway connection (namely Gisborne), and many other places that never received railway connections.

At the same time, NZ was one of the fastest adopters of the automobiles, second only to America.

I think viable cars and airplanes had taken another 25 years to arrive, NZ might have had a much more complete railway network, with a much better chance of surviving intact into the modern era.