Miller himself discussed how his definition of tragedy differs from Aristotle's in his article "Tragedy and the Common Man" ; the link is listed below. In this famous article, Miller defined the tragic hero as one who refuses to remain passive as he attempts to achieve his rightful place in the universe. This refusal, Miller contends, is what Aristotle called a flaw, but in actually is an inability to compromise one's integrity or vision. You might give the article a look, and see how well Willy Loman fits Miller's own definition of a tragic hero and how well he fits Aristotle's.
Aristotle's idea of tragedy refers to the downfall of a hero who is above average. The hero in The Death of a Salesman , Willy Loman is really a low ( of humble status) man. He does not inspire fear in the mind of the audience. He brings about his own downfall by his lack of self knowledge. But this is not to be compared with the downfall of Oedipus of Sophocles . The downfall of Oedipus concerns a whole city. But the downfall of Loman only affects his own household . Loman reminds us of Galsworthy's Falder who is a counterexample to Aristotle's conception of tragedy. There is no Fate or Nemesis involved in the tragic downfall of Loman. Lastly, Loman's fall does not rouse pity and fear to cause the catharsis of such emotions at the end of the play. The unity of time and place is also not maintained as required by a tragedy of Aristotle's definition.