the only problem i can see with using a computer supply is that some of the cheaper ones only regulate the 3.3 volt and/or 5 volt side of the supply and base the other voltages off that one.
if you just use the 12 volt off the computer supply, the regulation isn't any good because the regulated voltages are basically unloaded. so what you end up with is a 12 volt supply that may vary wildly or stay low (like 10 volts) since the supply thinks there is no load at all.
the peter chou arcade supplies are the same, they regulate only the 5 volt. the 12 volt goes really low without a 5 volt load if you put a load on the 5 volt line, the 12 volt pops up to 12.
a wall wart or laptop power supply would probably suit just fine.