Neither of the hosts would call themselves anarchists if asked. Mark believes in a government limited to police, courts and roads. Ian could technically be called an anarchist in that he believes that all three of those functions could be better provided on a voluntary and competitive basis by market processes, than by governments.
It's not "anarchy" in the mainstream/pop-culture idea of the word, but it can be accurately described as free-market anarchism. Ian, however, would prefer to be called a "voluntaryist" or "freemarketeer" simply because the term "anarchy" has so much baggage and misunderstanding attached to it.
*My comments are, of course, subject to correction by the people for whom I spoke.