The Ground wires serve much more purpose than anti-static. The primary reason you ground everything (especially in a cabinet like a MAME cabinet) is for safety reasons.
For example, if your monitor frame wasn't grounded and there was a short between 120VAC and the monitor frame, this can pose a electrical shock hazard to the user as the monitor frame will now be energized. Same thing with other controls.
Also, even though some controls will have their own +12VDC and +12VDC RTN lines, grounding may be necessary for proper operation. (See Sound and Car Amp post) for more information regarding this.
In your case, the ground is primarily used for safety (especially if there are metal components) and for anti-static purposes.
A rolling plastic ball and build up a lot of static charge (up to 50-100kV) which can damage both the electronics on board the roller and the computer it is connected to as well.
So it is VERY IMPORTANT to make sure that GROUND lead is attached ! ! ! !