The fact that a sizeable minority of libertarians are anarchists should cast doubt on a model that places them on opposite ends of a spectrum.
Brin is probably using "anarchist" to mean the movement that goes by that name, and not merely the adjective meaning "anti-state".
But some right-libertarians also call themselves anarchists (though left-anarchists take objection to that).
This is a great article at Aeon magazine. The author argues that the new ideological dichotomy is going to be between people who have great faith in technology and human innovation (Up) and the people who believe that humans are much more tied to their biology and the Earth (Down).
LW of course is a very Up community.