Everything
What genre isn't covered in Hyperion? (We'll play a few games of table tennis with our android servant while you try to come up with answer.) It's science fiction at its core, but within its tales is everything from adventure to mystery, horror to romance, quests, war, memoir, and more.
This seamless blending of genres makes Hyperion more of a character-driven story. Each character has his or her own life, motivations, and genre he or she fits best into. No one is the same, no one's experiences are the same, and different stories are better served by different genres. It makes more sense that way. After all, could you neatly plug your life and the lives of everyone you know into one genre?