OpenGL is a multi-platform standard for graphics, whereas DirectX limited to Windows and is proprietary to Microsoft. You can learn more about it here:
http://www.opengl.org/about/overview.html
but that's not really that important. The important thing is that since Dominions 2 uses OpenGL, you need a set of drivers for your video card that have good OpenGL support. It's possible that the issue with your friend's machine is that the drivers he is using for his Rage Fury are old, or that the chip itself may not have good OpenGL performance.
Make sure he goes to
http://www.ati.com/support/driver.html
and downloads the latest Win98 drivers available for the card.