I think Amazon are playing a global game with their Prime service, not only do you get preferential service on deliveries for purchased goods you also get a big library of films and other TV content to access from your computer as part of the same package. It's a different take on the bundling of services that we have come to expect from other Media/Telephony companies. So a bit like Sky offering existing SkySports users F1 for free, the rest of us have to buy the whole package although we only want the F1, Amazon have a variety of hook in points to draw us into the Prime service.
I'm sure they also see themselves as a content provider to other TV outlets around the world, as in the case of 'Ripper Street' - a BBC drama that got dropped which has now returned, thanks to Amazon production money, and has been sold back to BBC to screen in Britain for many £m.
They are probably looking at underwriting a lot of the costs of the new show with individual TV deals worldwide, the original Top Gear had a global following - so why not this new series? Only time will tell if both parties can pull it off.