It's not extremely useless when you consider most programming languages cover multiple PL paradigms.
Functional languages are a spectrum. On one end you have pure functional languages like Haskell where you're forced to use functional algorithms for all computation, but there are languages in the middle of that spectrum like C# which support a bunch of functional language constructs (take a look here for a selection: http://www.codeaddiction.net/articles/13/lambda-expressions-... ) even if they aren't purely functional.
My argument is, any definition of functional programming that ignores the mid part of the spectrum is useless, as it ignores that most languages do not strictly follow a single approach like Haskell but allow you to adapt to different styles (i.e. most programming languages are multi-paradigm). Even F# and Ocaml allow you to write in an imperative style if you so choose, and many people would class them as 'functional' languages.