Technically you need a registered company to "sponsor" you, but it can be your own company, where you are CEO and have 100% ownership. In the end, it's just a formality, the visa is granted on a personal basis. Compared to H1B where USCIS relies on a company to establish your credibility as a skilled worker, with O-1 they evaluate credibility themselves via multiple factors mostly involving peer validation (i.e. publications, articles, etc).

So yes, technically you need a job offer for O-1, but it's just a formality. Personally, I agree that it doesn't make much rational sense either, but then again barely anything makes sense when it comes to (US) immigration laws.