Well yes and no Urban. You said "the one where anyone can flick on the TV to watch football, British or American, and know exactly what they're going to get... how many players, how long it's gonna last, how the scoring works...".
If you use the word "football" as an umbrella term, under that you can have American Football, Soccer, Rugby League, Rugby Union (those 2 can be really confusing!), Australian Rules, Gaelic.......... Added to that, there are still different forms within each category, e.g. 5 a side soccer, "flag" US football as a no-contact version, Rugby 7's
So using the word "Paintball" as an umbrella term, we could include Concept/Sup'air tourneys, woodland tourneys, scenario games etc. And though maybe the international & major tourneys would usually be the same format e.g. 7-man sup'air there would still be events of different team sizes or formats e.g. 3-man or 10-man, or hyperball.