That's the article for "anarchism", not the article for "anarchy", which is what the OP has clearly been talking about this entire time. Surely you didn't link the wrong article on purpose to disingenuously support your point.

Here's the correct one, if it's difficult for you to find: https://en.m.wikipedia.org/wiki/Anarchy

And here's the relevant bit:

"Anarchy is often defined synonymously as chaos or social disorder,[10] reflecting the state of nature as depicted by Thomas Hobbes.[11] By this definition, anarchy represents not only an absence of government but also an absence of governance. This connection of anarchy with chaos usually assumes that, without government, no means of governance exist and thus that disorder is an unavoidable outcome of anarchy."

So, clearly, yes, by one widely accepted definition, "anarchy" does mean a system with no governing bodies or political structure of any kind.

That article also mentions anarchism, of course, but I don't care how a few political theorists in their ivory tower define the word, because that's not how word meaning is determined among speakers of a language - it's determined by continuous negotiation and agreement among speakers, and, currently, the most accessible default definition of "anarchy" for most speakers, OP clearly included, is "the absence of all government and political organization; chaos".