Yes, the state is a monopoly of force, by definition. It is the only entity that can create and enforce different rules by its own rules. What I mean is that it is an entity which outlaws the creation of other rules and enforcement of those rules in its territory and gives monopoly power over that market (the market for protection and courts).
That is the basic role of government: courts, police, and national defense, all of which are monopolies.
Now, does this prove that governments and monopolies are inevitable? No. Governments, as monopolies, arose only because people would agree to some kind of singular force dictating their lives. From there, governments only grew in power, creating more monopolies of its own (i.e. today the post office is a government monopoly).
However, an anarchy can exist. All that it requires is a group of people who don't want a monopoly of rules and ability to enforce those rules. Instead, these people can hire different protection agencies and private courts. In fact, I believe that's the way to fight back government today. Forget about painful revolutions, riots, etc. All we need is enough people who will deny the monopoly power of government and will create businesses that will compete with government monopolies for business, and yes, protect us from the government for not following their rules.