Alright, here's how you can get your polys and textures lookin all nice =) You have pretty much the same system configuration as me, so it should work well.
Anyways, go to your Display Properties, Settings tab. Then click on Advanced to open a new window. I have Ati also, but yours may look different here... but select the 3D tab. Select the Direct3D box, click the "Use Custom Settings" box, and click the Custom button. Here you can tweak the Anti-Aliasing and Filtering Settings to whatever you like. You can google these to find out what each does if you don't know already. Filtering will make the biggest difference (making it look like my screenshots). Beware though, as turning these settings up can cause a performance hit, and potentially mess with other graphics (by forcing a certain mode instead of letting the application choose). After you have changed these settings, just run GiriGiri normally.