Hey, this is my project! :) I am surprised it got posted here, but I am also glad to see people are interested.
One note on the title of this post: Elm compiles to HTML, CSS, and JS. Not just JS! I think this actually an extremely important distinction! It differentiates the project from templating libraries which still ultimately have you think and write in HTML. It also distinguishes it from scripting languages (like CoffeeScript) which also only address part of the problem. With Elm, you shouldn't need the mental model imposed by HTML and CSS which I think will be a really great thing.
Thank you! And yes, that has been a really good way to test the language out. I don't want to add it to the examples because I use some internal-only functions to make it work nicely. It's also not terribly instructive. You can see it at (http://elm-lang.org/edit/Elm.elm) if you really want. Due to some implementation issues with Element sizing and some Element abstractions, there is some suboptimal stuff in there, but I am working on it. It should be shorter and prettier when the language and implementation gets more mature.
For instance, I am really unhappy with padding/margin, so that almost certainly come out. I have a nicer abstraction in mind that should solve HTML's problems with padding/margins/positioning. I can't say it will happen soon, but it's on the way.