Mystery
Well, no brainer with this one. Detective novels always fall under the genre of Mystery. A crime is committed, the detective has to follow a string of clues to uncover the mystery, and the crime is resolved in a suspenseful climax at the end of the novel. But Red Harvest doesn't quite fit into the mystery mode. The Op solves the case of Donald Willsson's murder on Chapter 7, about 70 pages into the novel. And there's still another twenty chapters left to read, so we're not even halfway through the story yet.
Psychological Thriller, Realism
The Op's job is technically over after he figures out that Albury murdered Donald, and yet the Op decides to stay in town to clean up the city for good. So the rest of the novel turns into a psychological thriller where the Op pits one mobster against another, placing them each under pressure to see who cracks first. And throughout the novel, Hammett focuses on presenting a realistic, authentic portrayal of the ruthlessness and corruption of the 1920s American society.