“Patriarchy” is a floating signifier. It has no clear meaning. Indeed, it means whatever is convenient for it to mean in any given context. “Patriarchy” is furthermore a thought-terminating cliche. Instead of carefully thought out social analysis the Patriarchy is deployed as a non-explanation.
The Patriarchy is a useful non-concept for feminists to deploy to avoid ever holding any individual woman accountable. It’s not her fault she’s enforcing traditional male gender roles, it’s the Patriarchy. She couldn’t possibly be the abuser in the relationship, and even if she was it’s not really her fault it’s the Patriarchy. Don’t be angry at mothers who have their baby boys’ foreskins removed without anesthetic, it’s the Patriarchy.
The Patriarchy is a parody of class analysis. In this regard it is like, nay is, a conspiracy theory. Instead of naming an exhaustively analyzed and theorized capitalism, conspiracy theories decry a shadowy, conniving, amorphous Other. Conspiracy theory and Patriarchy theory inculcate paranoia and fear of this Other but offers no constructive response to combat the evil it describes. Patriarchy theory groups all men as the oppressor and all women as the oppressed. It thus resists intersectionality by smoothing over the many cases where a woman has power over a man or boy.
Patriarchy theory is false consciousness. It’s not even a particularly useful tool for analyzing women’s issues, let alone men’s issues.
That Wikipedia article is one of the worst offenders as it freely confuses the anthropological sense of “patriarchy” which is quite clearly defined.
Your definition adds something that no other definition I’ve seen before, including Wikipedia, specifies: powerful men. This ambiguity of multiple, conflicting definitions is exactly what I’m talking about.