The the motherboard power switch connection would be routed to a regular game button, probably located next to the original cabinet power switch. (that switch would still be there, but would be used to cut power to the entire box).
This is how I power my cab. I got an extra red (nothing like
a big red button) that I used to hook to the motherboard
where my PC on/off switch used to hook to. That was a
momentary switch so I figured it could serve the same
function and it does. I actually wired my TV do do the same
(see my website if you want to see how) but later
realized my TV remembers power-on and channel settings
when I unplug it, so I just route everything to a single
standard power strip bar use that to power on everything
and then the red button (now mounted on the rear of my CP box)
for the PC.
Ok, so it's two buttons not one but still the best I've got
w/o buying a smart strip...