Learn English – Is more than one “nor” after a “neither” correct

No, it wouldn't. The order can either be

I am not X nor Y nor Z.

Or it can be

I am neither X nor Y nor Z.

Or even

I am not X and neither am I Y or Z.

Let's simplify the sentence. I think this is the root version of the part you are interested in:

...neither lies in a valley NOR operates as an inn.

Your question is about the insertion of the parenthetical "(has ever operated)." Could it have an "or" in front of it? Should it have an "or" in front of it?

It is a little unusual, but not against any rule I know of, to have an "or" subclause nested inside a larger "NEITHER-NOR" structure --in fact this very same sentence has one earlier ("in OR near"). It has the potential to make things confusing, but in this case the parentheses would help eliminate the ambiguities.

Should it have an "or"? In this case, although the final meaning is the same, I would read the author not as eliding the "or" but as using the parenthetical as a direct modification of the meaning of "operated." Again, it's an unusual choice, but not technically a "wrong" one. I personally find the passage stylistically acceptable but a little old-fashioned. Modern style prefers simpler sentence structures. This older style, with more convoluted sentences, is a little baroque, but it does give a distinctive character to the author's voice.