In short the state is that body by which the individual capitalists come together and form a larger block to work in their common interests. The most important common interest is the suppression of the working class. If the state did not exist the libertarians would have to invent it. To finish with a brief discussion of what defines anarchism. As I have already said the dictionary does not.
Anarchism is above all defined by what anarchists have said and fought for.
Right from the start anarchists have been socialists. The 1st International was an explicitly socialist body that included anarchists, Marxists and others. At the same time in the USA anarchists were involved in the trade unions. From the start anarchism was a working class revolutionary movement. The biggest single anarchist event was the Spanish revolution of 1936.