It makes sense when you understand the origins, "libertarian" as a phrase was coopted from socialist-libertarians (now called anarchists), and is full of contradictions and hypocrises, mainly the one you mentioned about private property (in the economic sense of the term), controlling economic organizations as a dictator and owning their collective output as property. Not to mention this type of property is pretty anti-social can only exist with a massive bureaucracy and violence apparatus (courts and cops) which also contradicts their ideology.

I mean, their foundational philosophy is Ayn Rand, a fiction writer? The whole right-libertarian ideology is a joke compared to the intellectual rigor of anarchist theorists like Kropotkin, Bakunin, Malatesta, etc.

Especially in a world where the entire global economy is controlled by capitalists, it looks silly and just ends up affirming capitalist rule, like the OP has pointed out.