Yes 18 GA is the same as 18 AWG (American Wire Gauge).
For LED power, you'll be fine with the 20 or 22 gauge wire.
When talking about power and 18awg wire for arcades, its talking more about power for actual arcade machines, such as the +5v, -5v and 12v used in arcade machines.
For Mame, you'll be fine with the 20 - 20awg cable.