In 2019 170,000 thousand people visited the Cook Islands which has a permanent population of just 17,000. It's already just a large air travel and hospitality and tourism industry. They clearly have infrastructure. 17,000 also doesn't include the people who travel seasonally or temporarily for work.
Resources come from other islands and international commercial development. They aren't alone. The concept of transportation and travel exists.
May as well claim that a small town in the middle of the US is so small and primitive that it couldnt possibly be a hub for vehicle fuel and overnight stays. 
From your own source, Tom;
"
Rarotonga International Airport is capable of handling aircraft up to Boeing B789’s and B747’s. The Terminal has two gates that can accommodate two international aircraft at a time. The apron can be congested at times but apron can accommodate up to 3 internationals provided two aircraft are of medium category and the other a heavy category aircraft. Because the Terminal is small, there can be congestion at the check-in area if there are 3 international airlines checking in at the same time and at screening".
Hmmm.
Probably needs a little investment in the infrastructure to be a DXB challenger, doesn't it? Shame it can't find the zillions of petro-dollars that the middle-east could lay its hands on. And cheap aviation fuel would also help, like Dubai has it oozing up through the sand. And then, of course, there's the real estate; lovely map, and it does indeed have a good runway, but there isn't really much more than that is there. Where is it going to expand into? Demolish that town, raze the forest, drain the swamp, flatten the mountain or landfill the lagoon?
Plus, the Santiago-Auckland service doesn't actually need to stop there, does it?
Really, the only thing in its favour is the marketing - "
Don't just book it; Cook it!"