A play. Shakespeare's plays are intended to be performed on stage, and that makes them plays. The fact that the characters speak in poetry a lot of the time is not significant.
There are dialogues, often in poetry but also in prose which are written and are not intended to be performed on stage. These are sometimes called poetic dialogues, or, if they really strongly resemble play form, closet dramas.
They were called "groundlings."
Actors. The performers in any play are called actors.
Shakespeares "Othello"
The audience
Miranda
'If spirits can assume both form and suit,'
memorable characters
They were called "groundlings."
Actors. The performers in any play are called actors.
They would heckle the actors and throw fruit.
Shakespeares "Othello"
The audience
hamlet
Ophelia
Julius Caesar is generally called a tragedy. Although it might as easily have been called a history.
Julius Caesar
Romeo & Juliet