A healthy response to news of another compiler for your new language is, "Wonderful! People are demonstrating their belief in the future of our language with a big time investment! Another compiler will help us validate our language specification, which will be badly needed when we go to ISO to ask for a Rust standard Working Group."
It is just possible that a second compiler could be twice or (as happened with Pascal and C++!) 100 times faster. Faster builds would mean thousands of hours saved for users of the language—even, potentially, for people working on the old compiler!
A second implementation of the standard library could offer similar benefits.
More implementations is an absolute prerequisite to language maturity. All languages not doomed get them. It will be a net good for Rust not to be doomed.