If I had to guess the motivation, it would probably be that:

• Rust is a systems language known for performance and correctness, which makes it a good candidate for their stated goal of having a competitor to encourage performance and correctness within Prettier
• Rust is popular and relatively well-known among open source developers, more so than any comparable language except maybe Go
• Rust is a hip language that probably added some free publicity to their announcement

So cool. Curious, Why do they need to specify that the project has to be implemented in Rust?

Possibly because some people think that, much like MongoDB, Rust is web scale.