With that reasoning you could claim addition is impure, because time() + 1 changes over time. map is definitely a pure function. If you apply it to impure arguments, of course the result will be impure. The point in FP is to avoid using 'time', not 'map'.
Let me repeat: you used an introductory sentence as a "definition" of FP and are overinterpreting it. If you read later you will see:
> Functional programming languages, especially purely functional ones...
So Wikipedia distinguishes functional programming and pure functional programming. In fact there is a separate article on pure functional programming, which says that destructive modifications are "excluded", not just "avoided".
Functional programming does not have clear boundaries. You can have advantages of functional programming even if you introduce _a bit_ of FP style in a very imperative program. Conversely, you can write in very imperative style in Haskell.
Defining functional programming as programming with first-class functions is a consistent definition and could be used if not the fact that more people use the other definition (at least that is what the wikipedia definition and other online material makes me believe).