They don't fit the definition [1,2,3]. But I looked at the internet, and apparently many people consider neural nets to be statistical models, or "a kind of" statistical models.
What does it mean to be a statistical model? Deep nets are deterministic, for example. We can use them to model probability distributions, but they are not intrinsically statistical.
Well, deep neural nets are not statistical models, so shouldn't Chomsky now be at least a little bit happier with ChatGPT?