It uses the free Heroku instance with the free MongoHQ addon. That way if the site failed completely I wouldn't be out of pocket! If it keeps being used we'll either stump up some cash for Heroku or look at other hosting options. For now the free Heroku is fine, and the free MongoHQ addon still has enough space, particularly as we're storing so little.
There's no Ember or any similar framework, just a bit of jQuery that does the search filtering (which I want to improve - the entire site is a result of a 3-4 hour hack yesterday, plenty can be improved upon).
It's a small Ruby app that uses Sinatra, with Mongoid my gem of choice for talking to MongoDB. Uses the omniauth gem to authenticate with Twitter, and that's about it. Dead simple :)