Functional programming used to mean programming with first class functions and closures; they even put it in the name "functional"al programming (just like OOP meant program with objects, whether this involved classes or not).

So that is Lisp, the first FP in the 60s, and then the MLs of the 70s/80s. They knew about purity, and even preferred it (for things like list comprehensions, it is very useful), but were never very dogmatic about it.