In order to answer this question, let us first think about what Diamond’s thesis is. Diamond’s thesis is that it is geography, rather than genetics or culture, that make some societies richer and more powerful than others. People sometimes claim that societies become rich and powerful because their people are superior or their cultures are better. Diamond, by contrast, claims that the physical environment is what determines which cultures end up with wealth and power.
Polynesia is a great case study for this thesis because it was settled by people who were culturally and genetically identical. On p. 55 of the paperback edition of the book, Diamond tells us that the Polynesians’ ancestors all
...shared essentially the same culture, language, technology, and set of domesticated plants and animals.
Thus, the Polynesians all started out the same.
But then the Polynesians went and settled on islands with hugely different environments. This provides an excellent case study. If culture and “race” are what determine whether a society will be rich or powerful, all of the Polynesians should have remained identical. Instead, their societies became very different depending on the degree to which their environments allowed for intensive agriculture.
Because Polynesia allowed genetically and culturally identical people to settle in different environments, it is a great case study for Diamond’s thesis.