Pre-dates usable functional programming languages.
> immutability
Good point. Even if it doesn't have much to do much with functional programming, it did originate from FP languages.
> closures, generators, monads
These are really concepts needed to make up for the limitations of a pure functional layer of abstraction in a imperative world.
Yet they have been found to be much more widely useful. Closures as callbacks, generators as the basis for coroutines, and monads for error handling, not to mention things like C#’s Linq.
The counterparts of these concepts in the everyday programming world are fairly common sense design patterns that have been in use for fifty years.
The names and the beautiful theory for reasoning about them come from FP languages for sure, but that's the side effect of all PL theory being approached as FP theory, and are not fundamental to the 'functional' aspect of functional programming.