So many guesses have been made that I can't even remember what I've answered and not. I see that I've even answered some of the same questions twice aldready. So to clarify, this is what you know:
This is not a William Towns design, and as far as I can tell, it is a one-off.
There is no Sbarro connection. And it is not a Shark S1.
The car is not: German, Austrian, French, American, Italian, Swiss, Norwegian, or Swedish.
The car is: European.
The engine is not American, and not made by GM, Lamborghini, BMW, Mercedes, Jaguar, Rolls-Royce, Rover, Ford, Cadillac, or Oldsmobile.
It is not a rotary engine, but a relatively conventional, modern powerplant, made by a manufacturer that does not produce cars under its own name anymore. It's more interesting than that of a Volkswagen Beetle, but it is not Italian.
There, that about sums it up...