Genre is a word that refers to any category or identifiable type of literature or art form. Of course, there are many different types of genres around, and you might like to think about the way in which we apply genres much more commonly to films in our everyday speech and understanding than we do to works of literature. Thus we go to see a horror film or a romantic comedy, or an action film or a drama. These are examples of genres because they help divide up art forms into various groups or categories for us to compare and contrast them with other similar or like art forms.
Thus when we consider "The Doll's House," the simple answer is that its genre is a short story. The short story is a distinct literary form into which Mansfield's work falls which stands by itself and allows us to group short stories together so that they can be studied and compared.