Magical Realism, Coming-of-Age, Tragedy
We follow Roy Hobbs from being a hopeful, enthusiastic young rookie to being a frustrated, older guy, which might let us call The Natural a coming-of-age story. We see Roy go through traumatic experiences that he's supposed to learn from and that should result in greater maturity. But this is a coming-of-age story with a twist. Roy gets older but he doesn't really learn or change. He makes the same mistakes over and over. He's sadder but definitely not much wiser.
Every now and then totally fantastic things happen in the novel, things that are impossible but are presented in the context of normal happenings in the real world. That's magical realism, a Malamud specialty, doing its thing. In The Natural, for example, you've got Roy's magical bat that cracks like lightning and "causes" a thunderstorm. You've got Pop's unexplainable and weird illness on his hands. There's hallucinatory language and lots of dream sequences. These events all happen to a real bunch of people but are on the edges of we'd call reality.
In so many ways, The Natural is a tragedy in the classic sense: a hero falls from grace because of a tragic personal flaw. In Roy's case, the flaw is hunger—hunger for money, sex, and fame. Losing sight of what's really important in life, Roy gives in to these urges and it's the end of him.