I have another reply to this in this thread, and I stand by it, but I thought this might explain the use of the terms 'art' and 'spiritual' used in the article.
Western navigation is typically learned explicitly, meaning that it consists of a set of techniques that can be explained and carried out by that rational part of the brain.
This has many advantages, except that the rational part of the brain has less 'bandwidth' than the rest of the brain. The brain is a massively parallel machine that can respond to patterns in myriad ways, with the rational part being just one late addition, kind of like a calculator grafted on.[1]
The tiny bandwidth of the rational part of the brain is why we need calculators, why we take notes, have books, devise theorems and notations. We do this because it reduces the bandwidth required to reason about a given problem.
That integral you are trying to solve for homework in university, has just about as many 'parts' as the algebra problems you used to solve in grade 7.[2] Theres'a huge intellectual scaffolding underneath that integral sign, and many revisions of that scaffolding were developed, of course, but your brain in university does not have a bigger bandwidth than it did in grade 7.
But there are other ways of learning and knowing. And it's not so woo woo: implicit learning.
I bet you now how to catch a ball. How hard would it be for you to rationally[3] explain to me how ta catch a ball if I've never done it?
But you could trivially teach me to catch a ball, you'd toss it to me and give me hints until I caught it, and then I'd practice that till it became automatic. Then I'd have trouble explaining that to someone, but I could teach them in the same experiential way and so the skill can be passed on.[4]
This is why it's harder to teach a computer to catch a ball than it is to teach it to navigate.
So this 'spiritual' word, is hinting that the Polynesian navigators learned their navigation skills implicitly.
Relying much more on non rational (but not irrational) parts of the brain: recognizing patterns in nature, the position of stars yes, but tons of other clues that westerners have the luxury of ignoring because our charts and tables and GPS can just get us there already without all of that messy stuff.
Once a skill is acquired in this manner, it can be very hard to explain to someone else making it look uncanny to outsiders perhaps.
I think the word mystical might have been better than spiritual. But art fits pretty well for a skill learned in this way.
[1] https://en.wikipedia.org/wiki/The_Magical_Number_Seven,_Plus...
[2] https://en.wikipedia.org/wiki/Working_memory
[3] I mean a list of instructions that can be carried out so that success is guaranteed when correctly executed.
[4] A better example might be a sport like say surfing. It takes years to learn, and good surfers have a hard time explaining certain things. You just have observe nature (waves) and develop an intuition.