Biography / Autobiography
So here's the deal: The things in this book actually happened, so we've got to look at the story a little differently than we would a work of fiction. In a story that an author makes up, she creates a certain world for certain characters to live in, and she'll place meaningful little scenes and strategic ironies in little corners of the story to give us something to figure out.
This, however, isn't the case in this book. It's autobiographical (hence the whole really happened to Mitch bit), so instead of creating a world, Albom has chosen a certain way that he wants to tell us the story he and Morrie share. There are undoubtedly plenty of details and conversations that didn't make the cut, but the story is still fundamentally true. And insofar as it is Morrie's story as well, it's biography in addition to autobiography.
Another thing: Notice how most chapters have a little flashback or anecdote attached to the end. This is Mitch's way of adding meaning and variety to his story. In case you didn't notice, each little memory or story has to do with the chapter before it. In other words, this isn't two lives mindlessly documented—it's two lives carefully crafted to best demonstrate the lessons Morrie teaches, and the impact they have on Mitch.