TFA has gnocchi and matzo balls, so I think spätzle ought to be admissible as 0-dumplings (where a filled dumpling is a 1-dumpling). Proper dumplings would then be those dumplings with at least one layer of filling. Are there any 2-dumplings or higher, the dumpling equivalent of turducken?
(future work: classification of dumplings with handles, immersions of Klein Dumplings in cooking oil, ...)
Yes, dumplings don't need a fillings. But Spätzle are usually too thin to be called dumplings in my understanding. I'd call them a kind of noodle or pasta.
https://en.wikipedia.org/wiki/Sp%C3%A4tzle