I do not believe that the word "hegemony" appears at any point in this book. I have searched for the word using the Kindle version of the book and I have searched using the search utilities in Google Books and at Amazon.com. In all cases, no matches were found.
Diamond could well have used the word if he had been so inclined. One meaning of "hegemony" is something like "influence" or "power" that one person or group has over others. Diamond could have used the word, for example, in Chapter 16. He could have said that Chinese governments gained "hegemony" over the entire region that is now China. However, it appears that he did not choose to use this word here or anywhere else in the book.