I know of two companies that sell movie theater schedule datasets (through data dump or API): Tribune Media Services (http://www.tribunemediaservices.com/) and West World Media (http://www.westworldmedia.com/).
I'm not sure that there are any other. It's my understanding that the main movie sites (Google, Yahoo!, RottenTomatoes, MovieTickets…) all get their info from one of these two companies. This is also probably why you won't find a free API with that data.
Because the trailers are on YouTube, I suspected that the info was scraped from Google (I believe these two companies have their own trailer hosting); however, that would then make the connection between that info and RottenTomatoes a bit tricky… Peter, do you mind sharing?
I'm not very familiar with backbone.js so it's a little confusing to me, but looks like models are being built. Here's what I can muster, this could all be wrong
* [Line 112] The trailer is using a YouTube API (https://gdata.youtube.com/feeds/api/videos?alt=json&form...) and then the movie title?
* [Line 184] Ratings coming from RT API (http://api.rottentomatoes.com/api/public/v1.0/movies.json?ap...)
* [Line 341] Theatres & Times from Yahoo (http://query.yahooapis.com/v1/public/yql?q=use "store://VZHvlyU81L6BFVGyE7CNhT" as pterodactyl.movietimes; select * from pterodactyl.movietimes where zipcode="<zipcode>" and date="<date>"&format=json) -- I have no idea what this is all about. Any insight would be helpful.
* [Line 405] The links that Yahoo API thing returns are then rerouted to go through http://www.qksrv.net/click-5632409-10576771?url=<buyURL&..., I'm guessing for OP to get some cash
Then there's google maps for the maps, so that seems to be where the data pull is coming from. Not sure what the origin of that Yahoo URL is though.
EDIT: I added line numbers from the showtimes.js file because HN reformats the links so you can't see them all the way.