Which graphics chip, specifically? If it isn't in the system specs, it might be mentioned in dxdiag (click Start, or WinKey-R, type in dxdiag and hit Enter, then in the window that opens, switch to the Display tab), Display tab.
In the video section of the options, try switching to windowed or fake fullscreen mode, and see if that makes a difference.
Does changing graphics options make a difference? Try changing the 'Quality Preset' to Very Low, then if that makes it better or worse, play with the individual settings to narrow down what the problem is. It doesn't really look like a texture/shadow issue, though.