Just because functions are first class objects, there are closures, and higher order functions, does Javascript deserve to be called a Functional Programming language? The main thing I think it lacks is Pure Functions, and it doesn't 'feel' like other functional languages, like lisp (although thats not really a good reason for it not to be a functional langauge...)
Repeating my own answer to a similar question,
There's no accepted definition of functional programming language.
If you define functional language as the language that supports first class functions and lambdas, then yes, JavaScript *is* a functional language.
If you also consider the factors like support for immutability, algebraic data types, pattern matching, partial application etc then no, JavaScript *is not* a functional language.
I'd encourage you to read the following related blog posts (and also the comments below them):