Like I said your pcs more than capable of running the game, but ATI cards tend to be better as DX stuff, and sucky at GL.
Catalyst 3.9 was the last ATI driver that had fully working GL.
Speaking of ATI your card doesn't appear to have an 'official' ATI chip - it's one that's made for certain manufacturers, normally for laptops.
If it's a laptop there's a thread in the FAQ for laptops with ATI/Nvidia chips, and you'll find a link to an app/driver that fixes shader problems.