I think Doge could still be correctly branded a ponzi scheme, since the returns for an investor is essentially tied to the number of suckers that buy into it after them. An early investor can take a "structured payout" by selling off the asset once the hype-cycle is creating more and more suckers who buy into the idea.
The fact that it was a joke has been diluted from the mass media, mostly due to irresponsible messaging by idiots like Elon.