I found out that this stuff is called "extreme beer", although, after looking at some of the definitions of extreme beer, I think I would call "women's beer" a particular subset of extreme beer. It has no hops and is not brewed for high alcoholic content, although it does seem to have more alcohol than regular beer. Why it seems to have this bigger "kick" than regular beer, I don't know. It's nothing I've done intentionally, so I wouldn't know how to re-create it or remove it.
Another name that can be applied to it is "ancient ale", though my beer-drinking partner calls it "African beer". We in Western societies think this skill is "ancient" because made beer this way for a thousand years, but in Africa, it's just "beer", and it's still made by women. They make it for their families, and also sell it in taverns called "shabeens".