Novel, Family Drama
First and foremost, The Moonstone is a novel. But what, exactly, is a novel? "The novel" is one of the most vague genre categories out there. Critics will argue all day about how, exactly, "the novel" should be defined, but suffice to say that a novel is a work of fiction, written in prose (as opposed to poetry), that is fairly long. Yep, sounds like The Moonstone fits that category. But it's certainly not structured the way most other novels are – the different first-person narrators and shifting perspectives set it apart from most other Victorian novels. So maybe we should invent a new, sub-genre for The Moonstone.
Secondly, The Moonstone is a family drama. We're told on the first page that it's a "family story" (18.104.22.168) that Franklin Blake thinks should be written down so that future generations of the family will know what really happened. Almost all of the major characters are members of the same family: Godfrey, Franklin, and Rachel are first cousins (yes, it was normal and acceptable for first cousins to marry in nineteenth-century England), Miss Clack is a distant relation, Gabriel Betteredge has spent his life as a servant in the family, and even Mr. Bruff, the lawyer, is an old family friend. Even though the family hires a professional detective, Sergeant Cuff, to find the diamond, the mystery is only solved by members of the family.