Just looking at their benchmarks, it's not particularly fast. es-build looks much better in benchmarks, but it's not written in Rust. It seems they wanted a tool in Rust just-because (experience on the team, preference foe the language...), and then only compared against those.
As for the language "based on Rust", it's likely bad wording due to them not being native English speakers.
esbuild is written in Go, which has similar "probably quite fast and easy to install" properties to Rust.
Compare that to the expected experience if it was written in C++ or JavaScript or Python or Java or ... All of those are either likely to be slow or painful to use.
One of the reasons few people do that is because the build process becomes much more complicated. It's also much more complicated to do any sort of dynamic loading which is not terribly uncommon.
As for the language "based on Rust", it's likely bad wording due to them not being native English speakers.