This play is both characteristic of the American style of the time and also fairly unique. An understanding of the style of theater from which this play emerged allows us to have a very interesting look into it.
This play would be considered naturalistic, taking place over one continuous span of time and in one place. Furthermore, it features language that is natural-style prose (it sounds like how normal people speak). The goal of this is not just to show how people are but also why they are the way that they are. For example, we find out that 3rd Juror is impacted by the experience of having a son. Physical factors are taken into account as well, such as the temperature of the room. All of these are taken into direct consideration and impact the story.
The prevailing American style at the time was realism, which is much like naturalism, except that it is much more apt to deal with time disjointedly. However, it is very important to note that the first incarnation of this full play was, in fact, as a play for television. Although we are now accustomed to television programs using many locations and scenes like movies do, at the time it was far more common for teleplays and episodic dramas to take place on single sets, like a stage play. Therefore, the teleplay takes advantage of the limitations of its format to enhance themes and present a narrative that should take place in just one room.
On one hand, courtroom drama "who-dun-its" are certainly a favorite form of storytelling for American audiences. However, this play turns that on its head by not showing those involved or even investigating the case, but those who are sequestered to review the case, the jurors. This is a fairly abnormal choice, but what it does is change the focus of the play. We are no longer watching a play about figuring out whether or not the defendant killed his father, a fairly simple model, but rather we are trying to figure out how these men will learn to work with one another and whether or not they'll be able to overcome themselves and do what is right.