This part is taken out of context and out of time.
When this happens, the invasion has been going on for weeks already, and we've been fighting demons all over Azeroth and inside Dalaran. Its hard to really see this when you just join the beta and this is the first thing you do.
Its not like we go there and try to close the portal before anything comes through, like with WoD.
We go to a full demon-infested island with a full-blown demon city on it, from which they spawned invasions of the entirety of Azeroth, so the line seems appropriate, if a little dramatic.