It sounds like the book covers the troubled history (within the western lens) of social science and politic in their continual drive to redefine racial hierarchy categories by different attributes and social alliances/exclusions. Racial categorization is more tightly coupled to genetics at higher specificity and more loosely coupled at generalized racial categories. The closest genetic categorizations have to do with tribe and family. However, leaving just at the assertion that race categorizations are social constructs is a bit reductive. I can state that money is also a social construct, but it is also of real consequence. Class is a different social construct with realities roughly based on resources, political access, status, and pliable skills, also of real consequence. Racial categorization represents alliances by political preference or group preference within a society at a particular place and time, enforced using physical features as filters. An extreme reality of racial categorization is what tends to happen when countries go to war with each other. Accentuating the physical differences and merging them with negative attributes is practical because no regular person would want to harm someone they could see as their brother or friend.
Thanks for your thoughtful comment. Agreed that this is another way to look at the book, as one of the history of racial classification, while still examining the construction of a particular one. And to say it is a social construction is not counter to what you are describing, as the outcomes are social, and thus the search for some bio-explanation are for social outcomes, such as hierarchies. As someone once said, "I don't know if race exists; but racism surely does." So the biological reason may not hold up to science, but the social outcomes are as real as anything.