Apparently this cartoonist is not an "anarchist" exactly, but something called a "minarchist."
Minarchism (also known as minimal statism) is a political philosophy and a form of libertarianism. It is variously defined by sources. In the strictest sense, it holds that states ought to exist (as opposed to anarchy), that their only legitimate function is the protection of individuals from aggression, theft, breach of contract, and fraud, and that the only legitimate governmental institutions are the military, police, and courts. In the broadest sense, it also includes fire departments, prisons, the executive, and legislatures as legitimate government functions. Such states are generally called night-watchman states.That actually sounds pretty plausible. I tend to favor the Jeffersonian/Jacksonian approach that goes further, toward a state that uses its mechanisms to preference situations in which individuals own their own means of production, i.e., yeoman farmers or small businesses. I agree with their analysis, which is Aristotelian, that such a state avoids the chief problems of human politics.
However, I will state that this alternative doesn't sound so bad. Nozick is cited as a source for it, though, and he walked back his commitment to these principles later in life. I gather he felt that such a state didn't provide enough to ensure the protection of genuinely common goods, e.g., air quality or public education.