What? how? What about service workers (which constitute a major section of US workforce)? Do burger flippers at mcdonald's own their means of production? Cleaners? Waiters? Heck even truckers don't own their truck.
On the contrary, in the classical sense most gig-economy workers (at least those we associate with the gig economy) are not Proletariat - uber drivers own their car, AirBnB own their houses, Marketplaces (etsy, fiverr etc... which Amazon turk is nominally a part of) own the tools and knowledge to make whatever they sell.
Amazon Turkers are really not representative of the Gig Economy (a term that came much later then Amazon's Mechanical Turk) and at least for me I don't really think of them as part of the Gig Economy.