Earlier quoted context omitted.
"Anarchy" in that phrase is fucking wrong. Unsophisticated people assume that anarchy means "no rules", which is false. It means no rulers, not no rules. (More precisely, it means no non-rulers.) A better term would be "warlordism", if you want to emphasise the lawlessness of the financial class, or maybe "feudalism" to emphasise that the financial class and the political class are congruent.
Anarchy means "without government" or "without rulers". Seems fine to emphasize the government isn't acting like one.
I'll give you a gold star for deconstructing the word roots, but "anarchy" is a term of art.
The salient distinction is that society hasn't abolished rulers - it has merely replaced political rulers with corporate rulers.
Actual anarchy is hard fucking work. It's sustainable in small communities, but you have to sit through meetings where idiots ramble about some stupid shit that is important only to them. It is a prosocial form of government predicated on empowered consensus - which is to say, predicated on bickering. This requires far more from participants than warlordism, where all you have to do is obey the one with the biggest stick.
Anarchy devolves into shittier systems if the community fails to maintain it. It's a high-energy state. Warlordism doesn't devolve; it's the lowest-energy state. Government by primate dominance.
Letting Google and Facebook run your society is not anarchy, it's techno-warlordism. "Techno-feudalism" is less accurate, but broadly understood.