As others have explained, controllers (especially simple controllers like these) are supposed to work out of the box, with the standard input libraries of your operating system (DirectInput in Windows).
It seems like you're interested in knowing who makes these, so I tried a bit of google, and found that "RetroLink" is a registered trademark of a USA company called "Kool Brands LLC" registered in Reno, Nevada.
From what I could see in a low resolution scan of the back of another controller of the same brand, the bottom part barely reads "???????? and RetroLink ????? are trademarks of Kool Brands LLC", which corroborates this information.
They also seem to hold trademarks for "GameBully", "Robokit", "Exo-Guard", "Buck-Shot", "Retro gen" and "Sumoto". All game controller related.
They don't seem to have a website, but you can find more information about this company if you google them.
From what I see, they seem to be a tiny operation, probably solely a trademark holding company, and the RetroLink products are very likely rebranded generic chinese products.
I don't think they will have SDKs or other information like those you're looking for.
Googling a bit further, it seems like Kool Brands LLC is deeply involved with another company, which does have a website, called Innex. They sell RetroLink as well as other brands. If you have specific questions about the RetroLink products, they may be able to help you.