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.
You are generally right, but Clojure is a bad example, it is quite deliberately a “hosted” language, that can and does have many implementations for different platforms, e.g. ClojureScript.
Yea, that's true. I forgot about that. I did think of Clojure CLR, but I don't get the impression that this is an all that natural or used implementation so I ignored it. ClojureScript is obviously much more used, although it is still a "different" language.
Fable compiles F# to Python, Rust, and Dart now, too, in addition to JS. I haven't tried Dart or Rust, but when I tried compiling its output to Python it was actually quite good!