The Rise and Fall of the Third Reich isn't a biography in the traditional, literary sense of the word. Unlike most biographies, it doesn't focus exclusively on the history of one person's life. After all, although Shirer does tell us quite a lot about the life of Adolf Hitler, it isn't Hitler's name that appears in the title.
(Actually, Shirer wrote another book called The Rise and Fall of Adolf Hitler, which some of you WWII enthusiasts may want to check out.)
Rather than recount the life and death of one person, what TRFTR does is give us the life and death of an empire. As a work of history, it has many biographical elements, but they exist to tell us something about Nazi Germany on the whole. So, we can think of it as a kind of biography, but only if we remember that its focus is on the Third Reich itself, and not Adolf Hitler alone.