UPDATE: How to make this work with current builds of Vanilla (188.8.131.52)
After a long session of Googling, I've got this working on an up to date build of Vanilla. There are all sorts of problems with the documentation and the links on this plugin/app's page.
First off, as pointed out in some other comments, the author forgot to add "0" before the latest version number, so the big "Download Now" link goes to an outdated build. Version ".2" is the latest if you go by the dates, so download that to start things off.
Secondly, version ".2" is missing some files, apparently, as when I extracted it to my "/vanilla/applications" it didn't show up on Vanilla's dashboard, so I couldn't 'enable' it. To fix this, I created a new application folder based off of the skeleton folder that is at "/vanilla/applications/skeleton." Then, I merged the folder that version ".2" of this plugin/app with my newly created skeleton folder. Finally, the app showed up in the dashboard, but I got the error that this post is complaining about ("no 'index' view found").
To fix this, you need to create some empty index.php files. I don't know exactly what needs to be created, as I just downloaded an older version of this API (ironically, the one that the big "Download Now" link goes to), and then copied the "views" folder from that to "/vanilla/applications/views"
Whew. Anyway, it works now.