I wonder if it’s not the language that causes the products, but more that programmers that are drawn to functional languages are less likely to care about product.

That said, lots of things are functional: chunks of Facebook, Twitter, and Microsoft (and I assume Google) are written in OCaml, Haskell, Reason, and F#. Jet is built in F#. Jane Street famously uses OCaml, and Scala is becoming the standard language for hedge funds. Spark apps are usually written in Scala. Etc.