DNS is, for lack of a better metaphor, your roadmap to the internet. A DNS attack is compromising the 'directions' on that roadmap to point it toward something else. The URL is just a name you give the DNS to find the resource, it isn't the location of the resource itself.
So in this case, someone has gained access to the account 4chan uses to register it's location to the world, and done unpleasant things to it to point it where they please.
~M