The Aristotelian definition of tragedy involves a sense of transformation within the understanding of the character's perception of themselves and their world. Oedipus' depiction meets this standard, as the character seen at the start of the dramatic action has been completely changed by the events at the end of the narrative. The element of action in the play is also something that Aristotle would appreciate. Narration is not how the reader understands the fate and condition of Oedipus, but rather through action that helps to deliver the "catharsis" of the character. The reader/ audience ends up pitying Oedipus and fearing any potential of the same predicament falling upon their own states of being in the world.
In Aristotle's Poetics, he outlines the major principles of tragedy, citing Sophocles' Oedipus as the paragon of the form.
Aristotle's reasons are clear: to be the perfect tragedy the play must have a perfect plot. Oedipus follows the classic Aristotelian triangle of rising action, climax, and falling action. The play is full of dramatic irony (the audience knows more than the tragic hero) and verbal irony (the use of sarcasm, understatement, and overstatement). It has the classic "reversal of fortune" in which Oedipus thinks he is innocent, but then soon realizes he is guilty.
The play must also have the perfect tragic hero. He cannot be perfect; otherwise, his fall is not warranted. Conversely, he cannot be a criminal who rises to power--that too is unrealistic. So, Oedipus avoids these two extremes: Oedipus is a great man, but he also suffers from two great vices (anger and pride), so he is ripe for both greatness and a great fall.
Lastly, the play has the three unities, which leads to the greatest level of catharsis (purgation of pity and fear):
The unity of action: a play should have one main action that it follows, with no or few subplots.
The unity of place: a play should cover a single physical space and should not attempt to compress geography, nor should the stage represent more than one place.
The unity of time: the action in a play should take place over no more than 24 hours.