Diamond's major argument in this book is that geography, as opposed to race or culture, accounts for the fact that Europeans have come to dominate the world. Chapter 15 supports this argument by making a geographical argument for why whites succeeded in modernizing Australia where non-whites had not.
Diamond says that the case of Australia seems to prove that Europeans are superior to Aboriginal Australians. Europeans came to Australia and quickly created a "literate, food-producing, industrial democracy" (Diamond, p. 320). They did this in a place where Aboriginal Australians had failed to create such a society.
Diamond points out, however, that Australia was extremely unsuited to developing food production. It had no domesticable large animals and it had very few domesticable plants. He points out that Europeans who came to Australia had to import everything that they used to make Australia into the modern country it is today. They did not create a modern society in Australia, they imported it.
This supports Diamond's argument because it shows that Australia's geography was not suited to the development of food production and modern society. Such a society could only be created in Australia with the use of imported crops and technologies. This shows that it was geography, and not some failing of the Aboriginal Australians, that made Australia such a primitive society when the Europeans got there.