Does it really work well for other use cases? Obviously you can call it, but typically a web API has many more security issues to handle than a native API, so I'd expect there to be a lot of compromises a game developer wouldn't want to deal with.
Yes. The non-JS interfaces are Dawn (C++) and wgpu (Rust). The Bevy game engine uses wgpu and I think many others will do the same. You can't really generalise from "typical web APIs" in the way that you have.