Yes, it will run WoW pretty well.
It's got a good, fast CPU, enough RAM and a fast HDD. It's a bit light on the video card but WoW should be very playable on Medium graphics settings in raids. You can probably even reach High graphics settings if online game isn't too busy.
My gateway is DX with Vista. It has two sticks of 2GB ram. A stick went bad I guess. Bought two new sticks. But wont boot up if I but both in. If I run with just one of the 2GB sticks in it will boot and play. But I get d/c over and over when I play in some of the new zones. The computer lady told me its a bad bank on my motherboard. I just dont want to put more money in to this Gateway.