Everything else is a convenience and not a requirement for the functional paradigm.
Mind you, I do much prefer a Lisp or Scala to Javascript, but I face no trouble writing functional code in Javascript.
Out of curiousity, what other criteria would you apply?
You're more than welcome to have your own definition, but it's my opinion that it's too broad since HOFs exist in some form in languages like Java and Ruby and I wouldn't call them functional though like another commented said, languages are mixing paradigms nowadays (with the exception of Haskell!).
The big paradigm divisions were largely a thing of the 1990s; since then languages have become increasingly multiparadigm, so that it's almost hard to find a language that isn't nowadays. I think Haskell and Golang might be just about the last remaining standard-bearers of the league of one-trick ponies.