Anarchists operate within a utopian thought laboratory where everyone acts benevolently if simply left alone. In that imaginary context, the above “political quiz” has merit.
Does anyone need a king? No. But saying so does not make one an anarchist. It’s not as though monarchy is the only form of government. But that’s how anarchists see it. They regard any governing authority as “ruler,” making no distinction between arbitrary tyranny and due process under a constitutional republic.
The real question ought to be: do you need law? If you answer “no” to that, then you’re an anarchist. Of course, you’re also a slave, because anarchy isn’t an actual thing. It’s a vacuum into which the rule of the brute rushes in.