Hegemony in gender relations is a process, a historical relationship, and not a fixed pattern (still less a type of personality). The Western impact on the colonial world ruptured gender orders and initiated an endlessly complex struggle for new relationships. I have just been reading a biography of Mahatma Gandhi and one of the most interesting parts was his long path from a wholly patriarchal model of Hindu marriage towards a belief in gender equality, though with a very different inflection from Western feminism--for instance, Gandhi tried to get men to take up spinning as part of the anticolonial renovation.
Unlike the liberal state, today's multinational companies do not have a massive need for legitimation. They get their way mainly by simple coercion, and the collapse of the Soviet dictatorship has paradoxically cleared the ground for a reassertion of global patriarchy. States may become more woman-friendly; I think the Scandinavian states have gone a good way in that direction. But I have yet to see a woman-friendly money market, and it is global finance (stock exchanges, bond markets, futures markets, currency markets, loan markets, etc.) that is increasingly calling the tune in world affairs.