I have 8 pins on one 20A circuit and never had a problem with them all on and being played at the same time. I've put a clamp on ammeter on that circuit and it was pulling 15A. Just under the 16A continuous trip current.
The current rating of the main fuse, or what's written on the serial tag, is not what a game pulls when in operation. Typically it's 1.9 to 2.5A per game depending on game and if it has LEDs throughout.