People are keeping up with the hype of Elon's tweet so there's a demand.
In terms of fundamentals and use-case, DOGE is just a coin and that's it. No other use case.
You cannot complaint about the use case of Doge coin, there are many gambling sites that accepts them and that is the use case of Doge so that you can gamble without any worries and enjoy having a fun time without worrying much about the valuation. I do consider Dogecoin useful than thousand of other shit coins in the market which has nothing to do anything meaningful other than pump and dump.
So the answer is, Doge's price is based only on speculations.
So is the case with each and every coin in the cryptocurrency market, not just Doge even bitcoin is a speculative market and you call it by any fancy name, asset class, digital gold but it is speculative market just like Doge and i understand there are technical difference but overall it is all the same.