Family Drama; Tragedy
We call this bad boy a "family drama" for the obvious reason that it concerns a family. Over the course of the play, we watch the Helmer family disintegrate faster than Kool Aid in water.
Oh, and it's a "drama" not because it's full of more drama than a semester abroad program, but because it's a play—a piece of literature that's never fully realized until it's put on stage in front of an audience.
We also dub it a tragedy, though it's a bit different than the Greek or Elizabethan versions. Ibsen's version of tragedy is all about the individual vs. corrupt popular society. This is the opposite trajectory from a lot of previous tragedies.
(In Hamlet, for example, the good society has been thrown out of whack by the murderous, incestuous actions of Prince Hamlet's uncle. Hamlet must restore the kingdom to the lovely place of goodness that it once was.)
In Ibsen's version of tragedy, society was never any good to begin with. A Doll's House, for example, shows Nora (and maybe all its characters) trapped in a society defined by restrictive gender roles. In order to become more than a doll, Nora must shatter the cornerstone that her entire society is based on: marriage.
There you go: individual vs. corrupt popular society. In this tragedy, we don't get blood and death at the end; we get the death of a marriage and of the characters' old selves. Ibsen presents these things as the price of self-fulfillment: in order to make a freedom omelette, you need to crack a few marriage eggs.