No, it sort of acts like a collective term here, it’s just ’fish in general’, not a specific amount.
You mean unlike English, Swedish can use singular as collective? I mean in English "he eats fish", that "fish" is actually plural, right?
I wouldn't say that "fish" in the sentence "he eats fish" refers to a plural rather than to fish in general, no matter how much.
One can eat just fish without eating more than one fish. It can also be just a piece of fish.
If a man does not eat fish, would you offer him a salmon and a box of sardines?