What they're getting at is that the "state" is the entity that is socially accepted to have a "monopoly on legitimate violence." In this sense, the government asks you to pay a fine, okay, that's not violence per se, but if you decline to pay it, you may be arrested, or if not directly, then your continued resistance to further attempts to collect the debt could result in your arrest. All government action is predicated on the underlying threat of violence at the end of a chain of resistance to their orders, and that violence will be acceptable the population. Other parties can only use violence in accordance with the agreed limits from the state.

I guess it's not a useless paradigm, but it's more anthropology than political science. It's so fundamental and malleable as to be largely pointless from a policy standpoint, and it therefore allows everyone from cringey libertarians to literally insane SovCits to make bad faith arguments about how legitimate the state is.