How many sockets do you have total down there? You shouldn't have any problem running all 8 games on a single 20a circuit... Depending on the games, a 15a circuit may suffice if you're not running them for 3 hours or more at a time.
Most 19" rasters run at about 1amp... most 19" vectors run about 2-2.5 amp.
There IS a surge when powering up...so only power up one (or a couple) at a time.