I would think the line when a state has a monopoly on violence is when self defense is outlawed.
true, but it is shorthand & legal uses of violence by citizens are narrow (self-defense, immediate danger only etc). like free speech isnt totally free (limited in narrow cases)
Sport would be another use of citizen violence. That said most state restrictions on violence were asked for by the people. We demand a group that can only make laws, to do something.