e.g. If I am an Amazon affiliate, what is the term for Amazon's relationship to me?
I'd go with parent company.
A parent company is a company that owns enough voting stock in another firm to control management and operations by influencing or electing its board of directors.
Due to the fact that you're looking for a term that describes an independent affiliate, i.e. someone who is not controlled by the parent company, this wikipedia link suggests appropriate names for the four involved parties. The first one matches your position.
The industry has four core players: the merchant (also known as 'retailer' or 'brand'), the network (that contains offers for the affiliate to choose from and also takes care of the payments), the publisher (also known as 'the affiliate'), and the customer.
Affiliated companies are generally neither parent nor subsidiaries to each other, but share some common linkage, as a common parent upstream (not necessarily at the same level of parentage).
Usually the name given to the related company of an affiliate is affiliate. While there may be a number of possible relationships that describe the activity that Amazon may do to or for you, those probably complement your affiliate relationship.
Wikipedia suggests "merchant" for the company with whom the purchaser actually performs the transaction. To my mind, that's a reasonably intuitive term for most purposes.