Just because you own the tool you use -- be it a hammer, a screwdriver, or a car -- doesn't mean you own the means of production except in the very narrowest sense. The tools you use are worthless if there's no work to do with them, or nobody willing to pay you for that work.

"The means of production" in the gig economy is the marketplaces and apps. They parcel out the work to people to carry out using the tools they have at their disposal -- a car, a bike, a toolkit, whatever. It's established, much like a factory is, to break up the work into discrete steps to be carried out by people who are largely replaceable. In this case the app is just the replacement for the top-hatted capitalist factory owner.

AirBNB hosts are slightly different since they more closely resemble petit bourgeois smallholders and innkeepers rather than members of the proletariat.