Over C#:

* Garbage collectors often scare game developers since they can lead to hard-to-fix latency spikes.

* Rust has some cool libraries (specs, rayon, etc.) that let you safely parallelize computation.

Over C++:

* It's a memory-safe language, which instantly avoids tons of bugs.

* Library interfaces are usually higher-level in Rust than in C++, for various reasons (sum types being a big one).

* It's a much smaller language, so there aren't any dark corners that you'll randomly be forced to learn.

* It has an easy-to-use package manager, and I'm not sure where C++ is on that front.

There are many reasons, but to name a few important to me: rust gives performance on the level of C++, but with the memory safety of a garbage-collected language. It also provides protection against data races so that you can use concurrency with less chance of hard-to-debug issues.

For some, theoretically it's easier to train new Rust developers than it is to fix the bugs of new C/C++ programmers. Folks are trying to move the cost to training and dev bringup time instead of bug-fixing time.

Rust has other more technical advantages. But if you want to know why management is choosing it, it's because getting good C/C++ developers is a painful process nowadays.