In a way C++ is using higher-order functions conceptually too for polymorphic runtime dispatch. Because it uses vtables, which are lists of function pointers--essentially the object doing the dispatch is a HOF which calls one of the functions it has a pointer to.
All this is just made explicit, and the boilerplate OOP mechanisms stripped away, when you just directly pass first-class functions around.
I guess I just don't understand the connection between first class functions and multiple dispatch. I have a function "add()" that works differently for strings and numbers. How can I replicate that behavior with higher order functions?
The key idea is delegating the type-specific operations to specific implementations which handle them, and then statically (at compile time) choosing which specific implementation you're calling.
In OCaml (ReasonML) you have to pass in the implementations manually, but Haskell and Scala have the ability to automatically choose the implementation based on the types of the arguments, so that it looks dynamic even though it's static and type-safe.