Cool to see more people digging into Rust + Emscripten.
Not sure why the guide is using nightly Rust, stable has worked pretty well on Emscripten for a while. If you need to pass custom linker flags(which emscripten sometimes requires) you can do it via rustflag directive in .cargo/config.
We've been using Rust + Emscripten for some cross-platfrom targets(web, win32, osx, android and linux) and been pleasantly surprised with how straightforward+stable it's been.