Rust takes a lot of inspiration from functional languages, but I wouldn't call it a functional language itself. But yeah, not suited to every application.

Better start with this book, Rust will feel natural after that:

But you are right, it is better suited for one things and worse for other. It's not strictly functional, though, and most likely when it will have been maturing for as long as C++ or at least C# it will also have tools and features that make it better suited even for game development