I agree with Greg. Viewing Othello as a morality play would assume that Desdemona and Iago are both aware of the game they are playing. However, Iago is the one who controls and manipulates this game. At the very beginning of the play, Iago paints the image of Othello for the audience. Iago whispers many lies about Othello to the audience and whispers lies about others to Othello. His motivations seem unclear, and almost devilish, but Desdemona is not in an epic battle against Iago. Sadly, she does not know a game is even taking place.
Othello can better be understood as one of Shakespeare's great tragedies of love (see the JStor link I've attached below). Many scholars argue that Othello would be better titled as Othello and Desdemona, in a way that is similar to the titles of Antony and Cleopatra and Romeo and Juliet. Othello is frequently misunderstood and the core elements of the play are misconstrued. Each tragedy of love has external factors that are tearing apart the lovers (Iago is definitely one of these forces). The play is centered around the love between Othello and Desdemona, not the potentially demonic and angelic forces of Iago and Desdemona, respectively.
There are definitely aspects of this play that could confirm the idea that Othello is a morality play. However, this is ultimately a reductive viewing of the play.
I would say this statement is only of limited validity, for several reasons. First, while Iago might well be considered a devil, Desdemona is decidedly human. Second, they aren't really in contest. Iago is playing, and Desdemona, sadly, doesn't know she's in the game. It's only a valid here if it is a morality play in which the devil sets the rules.
Third, Iago's passion is so overwhelming that it really isn't a competition; he would lie, smash, destroy himself, just so Othello suffers.