Some have said that the focus of Othello is not the title character, as is the case with Shakespeare's other great tragedies, Macbeth, King Lear, and Hamlet. Is Othello simply too one-dimensional to be considered a great tragic hero? Does his seemingly unrealistic gullibility lessen our interest in him and his suffering?

I don't know how widespread that opinion is. In the distant past, critics faulted the play because it was a domestic rather than political tragedy. Thomas Rhymer called it a play whose message is for women "to look to their linen." In more recent years, this seems insulting, especially since it suggests that a male character cannot engage in meaningful action outside of government and war.
The play, like so many of Shakespeare's plays, deals in the way language shapes us and our imagination. It explores the complexity of love, particularly when one loves so much that one thinks that when one stops loving, "chaos is come again." Today, it would more likely fit within the genre of psychological thriller, as we slowly see Iago working upon Othello's confidence in himself and in Desdemona. In order for Iago's scheme to work, he has to play upon Othello's own powers of imagination and his understandable sense of being an Other within Venice, navigating the strange new world of domestic relationships and elite manners.
Another way we can approach the play is by analyzing the stories that are told. Othello narrates the story of his life to the men of Venice who find in them escapist adventures. To Desdemona, they are tales that elicit sympathy—both for Othello and for his gender. Othello loves her because she sighs and wishes "nature had made her such a man." These mutual sympathies lie in both character Desdemona's and Othello's courage and sense of not quite fitting in with social conventions. Desdemona is all too eager to leave Venice behind and follow Othello on his newest challenge.
The stories of the handkerchief also have a powerful effect, and like the first story of how Othello and Desdemona account for their love, the history of the handkerchief differs. Eventually, Othello tells one more story. In this one, he turns himself into the enemy of the state [a Turk] and stabs himself [the circumcised dog] to prove himself still a loyal servant to Venice worthy of being memorialized in the record. His political self must kill himself in order to punish his disloyal betrayal of Desdemona, a pearl of Venice:

And say besides that in Aleppo once,
Where a malignant and a turbaned Turk
Beat a Venetian and traduced the state,
I took by the throat the circumcisèd dog,
And smote him, thus.

In all these key scenes, the inner workings of a mind from a noble and free thinking individual into a tormented, murderous victim of language and false stories captures the modern audience. These inner dynamics are as compelling as Hamlet's or Lear's, to many audiences. In all three of these plays, the mind's capacity to know with certainty one of the most important questions we have [are we loved, is the world knowable, how do I respond when faced with a loss of self] are the central work of the play. In Othello, that occurs in Othello's mind.