From the introduction to the Folger library edition of Othello: "Othello is a drama of pathos and pity rather than a tragedy of character in which some tragic flaw brings about the doom of the hero. The latter concept was the Greek ideal of pure tragedy. Othello does not conform to this classic definition of tragedy."
Shakespeare's Othello cannot be considered a "sheer Greek tragedy." In fact, outside of the classical theater, very few plays can be considered tragedies in the Greek sense of the word (though some might argue for the French playwright Racine as an exception). The three major Greek tragedians were Sophocles, Euripides, and Aeschylus. The blueprint for tragedy, as we now understand it, was laid out by Aristotle in his Poetics, which stands as the first work of literary criticism. One element that is often forgotten by modern readers is that, for Aristotle, who was basing his writing on tragedies he had seen in Athens, these plays need to have unity of place, time, and action, something that is not found in most other plays, including Othello.
It should also be noted that Shakespeare and his contemporaries, while familiar with classical drama and mythology, had no first hand knowledge of the Greek playwrights or the Poetics. So while they had classical models, they were also creating their own forms.
All that said, Othello has a number of important similarities with Greek tragedy. The subject of tragedy needs to be a figure who is exceptional in some way. Many of the heroes of tragedy were kings (Oedipus, for example), royalty, heroes, gods. Othello is a successful Moorish general in the Venetian army. Shakespeare's invention of the character him both a larger than life figure and an outsider because of his race. Another key element is the tragic hero must have a tragic flaw (hamartia in Greek); for the Greeks, this was often pride or overreaching. It's a little trickier with Othello, as you could argue that he has several flaws, including distrust of his wife, Desdemona, naivete, and a trusting nature when it comes to Iago, who brings about his downfall. In ancient Greek theater, it is usually the gods who are punishing men, but here it is Iago, who is the agent of destruction, another invention on Shakespeare's part. Whether Othello's suffering and death evokes fear and pity (catharsis) in the audience is subjective.