The rules played are the WPA Blackball Pool Rules, commonly known as BlackBall.
Full rules can be read here, or downloaded here (requires Adobe Reader, which is downloadable here).

Here is a simplified summary of the key differences between pool rulesets:

Rule BlackBall Old-School/Pub
Break Two object balls must pass the middle pockets Two object balls must hit cushions
Object ball colour after potting on break Not decided:
Open table, with the next potted ball determining the object ball colour
Object ball colour is the same as the potted ball
Hitting a cushion with any ball after the object ball is hit Required (Partially):
Only if 1+ object balls are not potted in the same shot
Not required:
Tap-up snookers don't need to hit a cushion
Potting opponent's object balls during normal play Allowed, aka Skill Shot:
Must also pot 1+ object balls in the same shot
Not allowed:
Can only pot opponent's balls using a Free Ball
Following an opponent who fouled on their previous shot One shot carry, two shots:
First shot is a Free Ball, second shot is normal
Two shot carry, two shots:
First shot is a Free Ball with carry, second shot is normal
Time limit for each shot 60 seconds:
Polite warning from opponent at 30 seconds
Not restricted:
Take as much time as you like... is it Xmas yet?