For one, they have 3 PCI slots, so you may be able to add a newer GFX card into them. Also, 99% of the work MAME does (even with graphics) is done with the CPU. The Graphics card (or integrated graphics) is only used as a frame buffer and to output the graphics to the screen.
Here are two scenarios:
1. "OK-ish" CPU with awesome graphics card = Not so good for MAME (esp if it is a newer version of MAME)
2. Great CPU with some stupid intel extreme integrated GFX = Will work very well for MAME, even newer versions.
Its the CPU, not the GFX card, that you need to focus on.
EDIT: Email Andy Warne if arcadevga would be compat with the specs given. Dont know if ArcadeVGA will work in a standard PCI slot.