If we look at Euripides' Medea, which was originally staged in 431 B.C.E., from the perspective of Aristotle's Poetics, written at least five decades later, then we can only conclude that Euripides' play is a tragedy in the true sense of the word.
First, Aristotle labels Euripides the most tragic of the tragic poets (Poetics, Section 13). Second, Aristotle observes that tragedy should generate the emotions of pity and fear in the audience. He notes that one of the most effective ways to generate these emotions is to have the tragedy involve people who are related to one another:
"But when the tragic incident occurs between those who are near or dear to one another--if, for example, a brother kills, or intends to kill, a brother, a son his father, a mother her son, a son his mother, or any other deed of the kind is done---these are the situations to be looked for by the poet." (S. H. Butcher translation)
Soon after making this comment, Aristotle cites Medea's killing of her own children in Euripides' play as an example of this (Poetics, Section 14).
Aristotle also notes that the protagonist in a tragedy should be from among the famous noble families of mythology and that the person should go from good fortune to bad fortune. If we regarded Jason as the protagonist, then he goes from being the hero who retrieved the golden fleece to being a man whose wife, father-in-law, and children are all dead. Additionally, at the end of the Medea, Medea predicts Jason's death.
Thus, in my view, Euripides' Medea is a tragedy in every sense of the word.