In Wikipedia, his genres are listed as Baroque Pop and Popera. His dad in a PM interview said that Rufus began listening to opera at a very young age. No, he doesn't sing like that, but on the other hand, no one's melodies are quite or even remotely like his. Also, his string and horn arrangements (whether handled by himself or his partners in poperatic crime) are quite unto themselves, and always one of the elements that set him immediately apart from the field, the entire field.
In Michael Hill's beautiful bio at rufuswainwright.com, both the author's and especially the artist's words tell the story of Rufus's first self-produced CD and connected events in a most impressive fashion. It's reassuring that in this vapid rapid time there are still real artists in popular music.