I would've gone with the 310m one. It's almost equal in performance to a 9600m, which I've seen manage the game well on medium with my own eyes.
At first that didn't sound right to me, but the GeForce 310M is actually close to the 9600M G...the lowest model of the 9600M series...go figure.

Yea but my parents want to buy it locally... and I don't blame them. So it's gotta be either from Office Depot, Walmart or Best Buy.
It also has to have a screen between 14" and 15". Then, of course, a good graphics card. 300+GB on the hard drive and at least a 2.0GHz processing speed. Over 4 hours of battery life is preferred. A dual-ore, i3 or i5 is preferred. No more than $850. Preferably an HP, Acer, Asus, Dell or Gateway.
Can you find one like that oh Great Magical-Laptop Finder? I've been looking all freaking day and I can't find anything. XD
From the those three places with your price range and requirements, it's going to be limited. However, here is one you missed:
http://www.officedepot.com/a/products/491478/HP-Pavilion-dv7-4060us-173-LED/
...yes, it's a bit bigger screen size, but the specs are nice for the price. Radeon 5650, Triple Core CPU...it's a hell of a deal for only $700 and at Office Depot no less.
Here's a smaller notebook with a Radeon 5145...it does cost more:
http://www.officedepot.com/a/products/410757/Lenovo-ThinkPad-L412-4403-Core-i3/
....the Mobility Radeon 5145 is a renamed and slightly faster Mobility Radeon 4570. It'll get you some mediumish settings and is a bit better than the GeForce 310M.