Drama, Family Drama, Coming of Age, Tragedy
The fact that this is a play makes it by definition a drama, a piece of literature meant to be spoken by actors in front of a live audience. This particular drama focuses on the trials and tribulations of the Maxson family, making it a family drama. You could also view the play as a coming-of-age story, because it ends with Troy's son Cory advancing into manhood. Though it doesn't fit all the definitions of tragedy, it definitely meets many of the requirements. Check out our "Booker's Seven Basic Plots" entry for more.