I tried to play Quake II on my system with the ATI card, which didn't go very well. Software mode works, even with the 3dnow patch, but every single time I choose OpenGL and the game restarts to apply the setting, it just reverts to software mode. To make sure it wasn't the game itself, I tried it on a machine which is muuuuuuuuch newer, and OpenGL worked without an issue.
I tried 3 different drivers: one mobility driver (M6_12_12), the latest desktop driver (J5-30-1-b02) and a custom driver with a filename of W82560en. All drivers exhibit the same issue.

One other slight issue is the lack of 16:10 resolutions (obvious for drivers from this era). https://www.oocities.org/ziyadhosein/inf.htm describes how to set up custom resolutions, but after I edited the .inf and installed the driver via device manager, it didn't let me choose the custom resolutions.

Anybody who knows these iGPUs (or I guess relabeled laptop GPUs) well, please help!