I would say the three dramatic genre types that are most evident in Tape are Morality Play, Fantasy and Tragedy. Clearly, this represents a tragedy of the Aristotelian sort where it is not necessary the hero die for his failings (convenient since he is already dead). The Person is facing the painful consequences of having lied his way through life starting from when he was school-age and resulting in worrying, hurting and betraying the most beloved and important people in his life beginning with his mother:
WOMAN'S VOICE: "Where have you been? Do you know I've been looking all over? Jesus Christ! ... I went to the pharmacy! The school! I even called the police! .... look at me and tell me ...! Tell me right now!"
The setting is a fantasy setting where the dead are introduced to a darkened room with nothing but a lightbulb, a chair, a table, and a reel-to-reel tape recorder. Here, each person, after death, is kept until they have listened to every one of the lies they have told in any form whatsoever, whether to themselves, in thought, to another person, or "deep in [their] mind." The fantasy includes a collection of ten thousand tape recorded reels of lies for the Person to listen to.
There is a sense of this being a morality play although a central feature of morality plays--the personification of abstract qualities as characters, like Goodness or Virtue--is missing. Although, the Attendant might be considered a personification of an Angel. Morality plays personify the abstract battles humans wage between virtues and vices and present them as moral lessons showing which moral choices to make and why. Tape is a type of morality play in that--with the Attendant as a personified abstraction of an angelic power--the moral lesson against lying and falsehoods of all kinds shows the consequences of failing in and the value of succeeding in the moral lesson that is taught.