This question will open a great deal of discussion and I am not sure you will have a definitive answer.
Perhaps, you will have to piece together ideas to derive your own understanding. I look at modern drama from a thematic perspective.
Part of what defines modern drama for me is an emphasis on experiences and predicaments that have applicability to as many people as possible. Modern drama speaks loudly and lucidly to multiple parties, and can articulate struggle and redemption in a manner that makes it understandable to all in the modern setting.Its relevancy is effective in real time. For example, a reason I consider Beckett’s Waiting for Godot modern drama because it speaks to a condition of paralysis that can apply to human beings, as a whole. The Crucible is an example of modern drama because it speaks to the vision of the tyranny of the community and the hypocrisy that it compels within individuals.
This definition of modern drama can encompass works that apply to a particular culture of individuals.I consider Angels in America, a play that deals with thematic elements about homosexuality, an example of modern drama because it speaks to how one deals with death and the fear of it. Fences might be a work that is applicable to the African American predicament but it speaks to a larger conception of dreams and conflict within families. For me, modern drama has to speak to issues where there is a level of connection that can be evident to as many individuals as possible as something new in the human predicament is revealed.