So basically, the Duke's aiming to kill all the non-magicians, so that the genius magician Violet can take the throne, as a final "screw you" to his dad who thought that only non-magicians should be able to inherit the throne.
Kinda funny how right after that gets revealed, the first thing he wants to do is eliminate the Arbuthnots, because of their "inconvenient gift". Pretty sure that's basically what your dad was doing too dude, but I guess that's part of the point and what someone will shout back at him when it comes to talk-no-jutsu time.