What do you mean by "outside the .NET world"? F# is a .NET language (more specifically a CLR language). That question seems to be like asking "are Erlang and Elixir contenders outside of the BEAM world?" or "is Clojure a contender outside of the JVM world?".

F# being on top of the CLR and .NET is a benefit. It is very easy to install .NET, and it comes with a huge amount of functionality.

If you're asking if the language F# could be ported to another VM, then I'd say yes, but I don't see the point unless that VM offered similar and additional functionality.

You can use F# as if C# didn't exist, if that's what you mean, and by treating .NET and CLR as an implementation detail, which they effectively are.

There aren't many languages that can do server-side and browser-side well. F# is one of them!