The structure of the play is reminiscent of certain other works of literature from the period before modernism. Using symbolism and character pairs to structure the narrative which eventually becomes a (naturalistically developed) polemic on identity is also not something we'd usually see in works of modernism.
If we are using the term "modern" here to mean contemporary then we can talk about how the issues of dignity and identity are alive and well today, especially in theater. This play, in that regard, is still highly relavant.
A Doll's House has a universal theme which, to this day, continues to be debated: The role of females within the family unit. When the play was written, Ibsen basically defined the role women as a nurturers, entertainers, mistresses, and lovers. Nora "tainted" that role by attempting the unthinkable: To be useful.
Still, to this day we have several societal rules that are imposed upon women and are even more difficult to understand. For once, women are always expected to be nurturers and almost completely responsible of keeping their marriages interesting. However, in these days, we are also expected to be heads of household, to carry on with business and do a lot of things independently. While that is very factual and doable, we continue to see the focus set on women and not as much on males. We can definitely see the same happening in A Doll's House: Therefore, as a modern play, we can conclude that the same topics continue to reflect themselves from time to time in many forms of literature.
I think this excellent play was definitely very modern when it first came out, as the outrage it provoked amongst society amply demonstrates. However, as other editors argue, the complete change in the position of women in society and the way that we have moved towards a more equal balance of relations between men and women (note I said "more" equal) would rob this classic of the same kind of impact were it to be brought out in today's day and age.
I do not think that it would have the same impact today as it did when it first appeared in 1879. Women are very different today. They have separate checking accounts, pay bills, take out loans, and generally command the home. The play, if modernized, would need to focus more upon the dichotomy which exists regarding the relationship between Torvald and Nora. It, for me, would be a much more interesting play.
Ibsen's focus on a female protagonist in a play with a distinctly feminist theme makes the play very modern. Nora's attitudes towards her marriage and society's and Torvald's expectations of her are surprising considering the time period of the play -- the very traditional and conservative Victorian period. Granted, Ibsen is not English, but those attitudes where pervasive around the Western World.
I think that there can be much to take away from Ibsen's work as a one of modernist sensibilities. The fact that the central conflict of the work involves the fragmentation of a traditionalist setting makes the work quite modern. When Virginia Woolf argues that the essence of the modern setting is the idea of all "human relations shifted," this statement applies perfectly to Nora and Torvald. Nora recognizes this shift in her own sensibilities and Torvald fails to fully embrace it. To this end, the play is modern in how it articulates the "shift" that exists between human beings. At the same time, I think that the work is a modern one because it brings out the articulation of voice as one of its primary concern. The work makes Nora's voice extremely important, one that is worthy of articulation and bringing from modern to center. This helps make the work modern, and one that embraces the modernist ideas. In the end, the lack of totality that is presented in the work is also a modern notion. Nora leaves, but we, as the audience, are left in a state of not knowing. We simply do not know what is going to happen to her and to Torvald. This condition of uncertainty is also what helps to make Ibsen's play a modern one.