See my book "Playing for Prizes." The award process is multi-layered and historically unpredictable as to the results. If you're a playwright, you can submit your play with $50 to be considered. The script doesn't need to have been produced ANYWHERE and certainly not in NYC. The Jury that nominates the finalists is typically made up of 3 media reviewers, 1 academic, and 1 recent winner of the prize. Not all members of the Jury may have seen the plays under consideration. The Jury's recommendations can be superseded by the Prize Board, made up mostly of journalists, academics, and ex-officio members. Those Board members are not required to see or read the plays under consideration. Over time, the Board has come up with surprises that ignored the Jury's choices, some of them good, such as "A Cat on a Hot Tin Roof." The Board has also chosen to make no Drama Prize in some years, even if the Jury makes strong recommendations.
All of the major Best Play and Best Musical awards' history and methods are really interesting--NY Drama Critics Circle, Outer Critics Circle, Tonys, Drama League, and Drama Desk. At least, they were to me and the reason I researched and wrote "Playing for Prizes."