That's the goal from their perspective. Neoreactionaries are former anarcho-capitalists who want to break up the public democratic government so that they can implement private government.
As a side note, that linked article and the assumptions you make off of it (the article does not mention "anarcho-capitalism" or "private government") both seem wildly unbased, more than bordering on conspiracy. The evidence against Thiel is more or less tantamount to him funding a startup founded by Yarvin, but surely there could have been a plethora of non-political motivations behind that.