It's a psychological condition vaguely related to Tourette's, but Tourette's is a neurological disorder.
Arthur's is clearly a psychological condition that combines grandiosity with lack of impulse control, classified in the DSM-IV as number 312.34: "Intermittent Explosive Disorder" or "Episodic Dyscontrol Syndrome."
What makes Arthur's bad behavior sociopathic (but not psychopathic) is that Arthur NEVER expresses any genuine regret or guilt. Whatever he ends up saying in his Intermittent Explosion, he stands behind, whether it was appropriate or not, whether it was even TRUE or not. In fact, the less true it is, the more insistent he is that it IS true: "It MUST be true...because I was the one who thought it."
Arthur will never admit he's wrong. On the rare occasions he changes his mind publicly--such as reversing his decision that Patti LuPone would NEVER play Rose In New York--he makes the change in decision WHOLLY about himself: "Yes, Patti can play the part in New York--but only if I direct her MYSELF. Because without my direction, she'd be a failure!"