The bolded part is the important one - you can see this wording on other continuous effects.A monster that is destroyed by this monster as a result of battle is removed from play instead of going to the Graveyard.
I thought he was talking about Dark Magician of Chaos.[info]You can activate "Divine Wrath" during the Damage Step because it is a Counter Trap Card, so you may activate it to negate the effect of "D.D. Crazy Beast."[/info]It's a Trigger Effect, since it uses a chain. The OCG agrees on this point.