When answering this question, you must think about "man-made constructions" in a broader sense. You must think of it in terms of societal and governmental "constructions," not simply in terms of physcial things. The "construction" that allowed for an increase in population density was, to Diamond, the organized chiefdom.
Diamond argues that the presence of an organized, hierarchical government makes it easier to have intense use of natural resources. Hawaiian chiefs were able to make their subjects take part in "public works" projects like creating irrigation systems. These works made it more possible to do intense agriculture and thus to have a higher population density.
The more organized a society, the more it is able to feed a large number of people and cause them to get along peacefully together. This organized society was the important "construction" in Hawaii.