Aristotle, in Poetics, was very rigid in his defining of the characteristics of the tragedy. Aristotle defined the tragedy through six common characteristics.
"Tragedy, then, is a process of imitating an action which has serious implications, is complete, and possesses magnitude; by means of language which has been made sensuously attractive, with each of its varieties found separately in the parts; enacted by the persons themselves and not presented through narrative; through a course of pity and fear completing the purification (catharsis, sometimes translated "purgation") of such emotions." (Poetics of Aristotle)
Based upon this definition of the tragedy, William Shakespeare's Macbeth imitates the treachery seen during the period of kings. Not only that, these treacherous acts (as in the murder of King Duncan) possesses both "magnitude" (the death of the king) and "serious implications" (the belief that Macbeth is responsible for the murder of Duncan).
The language of Macbeth is "sensually attractive" (shown in both the elevated dialogue and soliloquies). Likewise, no narrative proves the language to be sensual, only the dialogue and actions of "the persons themselves" do this. Essentially, no one narrator is telling the audience the message; instead, the characters on stage are defining themselves on their own.
Engaged readers are drawn to the emotions of the characters. Some may feel pity and fear as the play progresses, while others may feel cleansed by the drama.
All of this said, one can justify that Macbeth is successful at following Aristotle's characteristics of the tragedy.