This sounds like a common mantra from people who love Rust to the point they'd use it even for basic scripting.
No, Go does not losing any mindshare to Rust whatsoever. Rust is an interesing choice when you need all these memory management tricks but treality is - in most cases you don't really care because Go is just good enough.
Add to this that developing in Go requires much less time and effort (in other words money) and you will see that it won't be replaces by Rust in areas of web dev, systems integration etc.
Rust is good for systems programming, embeded devices and so on.