Dittany - i think the term Patriarchy when applied broadly does have a specific meaning from feminist theory that I don't believe in, although I do consider myself a feminist (= a single intentional system imposed by men as a group because of a common belief in male supremacy with women's role in the system as victims or 'handmaidens').
Also implicit in the concept, I think is a view about the relationship between social and biological systems that sees them as much more separate than I view them.
So I don't see any point me saying "yes I believe in the patriarchy, as a "vanilla concept" (without these add-ons) because then I would immediately have to say 'but I don't mean x y and z...and I do mean abc'
I don't think it helps for clarity or respect for the integrity of the theory for me to do that. (you could rightly say I was misusing the term, imposing my own meaning etc...)
So, to answer your question I think we live in a world ruled by very few people, who are predominantly men. But the vast majority of men are not rulers. So I think it is not true to say men rule the world if 99% of them do no such thing - and an individual's nationality, class, education etc... is a much stronger predictor of how much influence they have than their sex.
I don't see it as a system, but lots of systems, biological, social and political meshed together. They are tightly linked to other factors - in particular technology and the changes in society it enabled, energy, demographics, the growth of cities, organisations, trade, work and the massive growth in economic output over the past few hundred years. So when you talk of "the Patriarchy" I see all of this as tied in. I don't think we can overthrow it but we have to change it.
Male/female inequality is one amongst other major problems with this society that human nature has not equipped us for - how to deal with the global problem of climate change, how to live well for 80+ years, how to reduce inequality but retain freedom.
It would be great if they all had one word explanations - 'greed', 'ageism', and 'oppression' for example and a clear moral cast of goodies and baddies. But I don't think they do.