Looks like Amazon has already taken down the page that explains how to define the controllers.json Controller Configuration File. Not sure what it's means, but I can't find info on it anywhere else on the Internet. The app submission section claims the file is needed. Do you still have the page, the first URL you list, cached?
I thought so to, but the samples with the sdk add-on do not come with controllers.json. Maybe amazon has decided the file isn't needed. Supporting any an all blutooth controllers is the best way anyways. I'm wondering what the original web page said.
The high ratings given to GTA 5 and the relatively low ratings given to Sleeping Dogs by these websites...
...are exactly why I don't trust a single thing they say anymore. Sleeping Dogs > GTA 5 easy.