Are HOAs considered a DIY government?

I'd say so. It sure looks, walks and smells like a government. They're often responsible for things that ought to be the local council's job, and have a tendency to enact rules which will lead to consequences if not followed (just being able to be fined by one, even if the rules are reasonable, sure does make one feel like a government). It's all on a smaller scale than the government-government, but that doesn't really make it a non-government to me.

Yes of course they are.