Purescript looks too good to be true. Does anybody know of any small projects that show it off? Don't see anything on GitHub...

I understand it's a moving target but, besides that, do any of the other languages in its niche really compete?

There are a few interesting projects in the contrib organization on GitHub:

https://github.com/purescript-contrib

I also like inquire.js:

https://github.com/concordusapps/inquire.js

Also, some slides and examples from a talk I recently gave, with a few (what I think are cool) examples of functional approaches to common JS problems:

https://github.com/paf31/lambdaconf

And a little game (needs some more work):

https://github.com/paf31/purescript-croco http://functorial.com/purescript-croco/html/