i do not believe stirner opererated on that definition.

here is maletesta's definition of the state, which i find far more useful for critiquing states.

“Anarchists, including this writer, have used the word State, and still do, to mean the sum total of the political, legislative, judiciary, military and financial institutions through which the management of their own affairs, the control over their personal behavior, the responsibility for their personal safety, are taken away from the people and entrusted to others who, by usurpation or delegation, are vested with the powers to make the laws for everything and everybody, and to oblige the people to observe them, if need be, by the use of collective force.”

i would go as far as to say that the entire anarchist critique of states builds on such a an understanding of states, and in turn becomes less coherent with a defintion like the one you are using.