Does Aristotle's schema of the elements of tragedy have any relevance today?
In order to discuss the relevance of Aristotle's definition of tragedy, we should first review that definition and break it down into its key parts:
Tragedy, then, is an imitation of an action that is serious and complete, and which has some greatness about it. It imitates in words with pleasant accompaniments, each type belonging separately to the different parts of the work. It imitates people performing actions and does not rely on narration. It achieves, through pity and fear, the catharsis of these sorts of feelings. (Poet. 1449 b21–29)
Aristotle defines tragedy as a genre in which a significant part of the main character (tragic hero) is dramatized ("imitates people performing actions and does not rely on narration"). Through watching the drama, the audience experiences "catharsis," a purging of emotions, which is felt while watching the downfall of the tragic hero.
We can take as a sort of case study the very famous Greek tragedy Oedipus the King by Sophocles. Oedipus is a tragic hero who begins the play as the respected King of Thebes; he became king by saving the city from the Sphinx. However, it turns out that Oedipus fulfilled the prophecy given to his parents at his birth: he would kill his father (Laius, former King of Thebes) and marry his mother (Jocasta, Queen of Thebes). This significant act occurred before the play begins, but we see Oedipus vow to find the murderer of Laius in order to end the plague in Thebes, inadvertently cursing himself. The action of the play revolves around Oedipus investigating and then learning the horrible truth of his past. As a result, the audience (and the Chorus) experiences pity and fear. The audience feels bad for Oedipus because it seems he has been cursed by the gods unjustly. We fear what will happen when he discovers his past actions. We pity him when he learns what he has done, when he blinds himself, and when he is exiled from the city. Oedipus experiences one of the most dramatic falls in the history of tragedy. After the play, the audience returns to their average lives, purged of the emotions felt during the play through the experience of watching Oedipus's downfall.
In some ways, this story may not seem relevant to us today because we are not as attached to ideas of fate as the ancient Greeks were. However, we do still experience tragedy and loss. We are aware in our own lives of falls from greatness or power. We suffer, and we are sometimes unjustly tasked with overcoming experiences that we feel we should not have to face. We also still feel catharsis when we watch tragic stories, whether real ones (news, documentaries) or dramatized ones (plays, television shows, movies). In more ways than one, the definition of tragedy posited by Aristotle applies to our lives and the forms of entertainment that we enjoy today.
Tragedy definition is quoted from Stanford Univeristy: https://plato.stanford.edu/entries/aristotle/#RheArt