I am not one hundred percent sure how they did it on the 31 Digital site because I didn't make it. My guess is that a pages was made for each "by name" and "by genre" view and the CataBlog ShortCode
[catablog category="movie"] was put on each page with a category filter.
So you know, this cannot be made with one static page, while CataBlog does let you make a catalog, it doesn't offer much for navigation. This is because WordPress itself has so many options and features I felt that people should leverage the built in navigation features of WordPress.
To create the pages you want you should put each CataBlog item into two categories, the genre and the letter grouping. For instance 'Art Studio' should be in the 'art' category and the 'A' category. Then you should make static pages for the 'A' category and the 'Art' category and place the appropriate ShortCode onto those pages. So for example put
[catablog category="A"] on the page you made for the 'A' category. Continue this for all your genre and name categories. Keep in mind you may also make a custom page template to list the links at the top of each page if you don't want to copy and paste the navigation code into each page.
Good luck and let me know if this solution works for you. Yes it is a bit of a setup, but once all the pages are made you simply manage the catalog and ignore the pages...which is nice. Also if you haven't already done so, please rate and confirm CataBlog works with your version of WordPress at the link on the bottom of your post. :)