Does the state have a monopoly on violence?

I think that is using the term “violence” to strongly. The state keeps the peace through laws and courts and possibly the threat of violence.

When I think of Monopoly of Violence, I think of the Third Reich, Secret Police (The Gestapo), Nazis and Jackboots.

American government is a bit more benign.

And yes, I see the definition you’ve linked to but I still think it’s too strongly stated.