The C++ is compiled to WASM. You can look into [1] to see emscripten there.

[1] https://github.com/ggerganov/whisper.cpp/blob/master/CMakeLi...

Maybe they meant to link to something like this:

https://github.com/ggerganov/whisper.cpp/pull/540

Web demo:

https://whisper.ggerganov.com/