If all you need is a computer that can play WoW, then I'm pretty sure both computers will do the job. Newegg's graphics card is the same as the one I own, and although it isn't the greatest, I don't have any complaints. Although I'm not sure about the graphics card, I believe that the i3 computer from futureshop is a better computer. It's processor is better and has double the amount of memory in its hard drive. The only thing I'm worried about is that on that computer, it lists the power supply as 300W. I don't know if this is an error, but that seems pretty low on that kind of machine. Needless to say, if you don't plan on upgrading your computer at all, it should still run fine when you get it. Unfortunately, I'm not sure what you mean by a "wireless chip." Do you mean bluetooth, or possibly wireless internet? Newegg isn't clear on either, but the i3 doesn't have built-in bluetooth. I believe that most desktops don't have built-in bluetooth anyway. All in all, if you don't mind the extra $60 and the fact that the 300W power supply probably won't let you upgrade your computer much at all, I'd go with the i3 from futureshop.
I believe that your cheapest solution would be to just upgrade whatever computer you have now, provided you have a copy of windows. Your computer doesn't need to be anything special. You only need a case with a hard drive and dvd drives (which I assume you have). If you replace your motherboard, graphics card, RAM, and processor, it may cost around $450 for something better than either computer. Instead of settling for a dual-core processor, you can get a quad-core with a better power supply, graphics card, and RAM. I recently upgraded mine for the first time, replacing all of these components at once (except the graphics card). Although it was a bit troublesome, I saved some money and got a better computer in the process. If you are interested, this may be your best option.