Like Odysseus, Cal Stephanides, or Oscar Wao, Dominick Birdsey is a man on a mission. Unlike most people in Connecticut, whose main mission is fighting their way to the yogurt aisle in the back of Whole Foods, Dominick's mission is a little more daunting: finding a way to take care of his paranoid-schizophrenic twin brother.
Dominick doesn't just want to help Thomas, though, he wants to cure him. Dominick wants to do other impossible (or at least really difficult) things, too, like absolve himself of the white guilt he feels because Native Americans lost their land, and find out who his real father is. So he's got his work cut out for him.
This isn't quite fighting a Cyclops or escaping from the Dominican Republic, but for Dominick, it's important stuff. Even his therapist buys into this, talking about "ancient myths" and "orphaned sons […] in search of their fathers" (47.254). In order to find his answers, he doesn't have to cover a lot of physical ground, but he has to travel through time. Not literally, but figuratively, delving into his childhood memories and the memoirs of his grandfather.
His story follows a typical hero arc—a tragedy, a fall from grace, and a redemption. It's a long, hard journey, full of pain, loss, and crazy old Italian women, but Dominick ends up earning his own happy ending. And for these reasons, it earns the dual genre prize of being both a tragicomedy (a tragedy with a happy ending) and a quest.