Amazon is one of the many places you can go online if you wish to shop for video games, among other things. They're huge and usually very reliable - they have a good reputation that keeps people coming back. So when people began to notice that some big-name games were being blocked from purchase unless you were an Amazon Prime member... well, it confused and annoyed a lot of people.
Games including FIFA 16, Far Cry Primal and Battlefield Hardline on both the PlayStation 4 and Xbox One were affected in the UK, and the label was applied to Grand Theft Auto V among others in the US store. This requirement was only in place if you wished to order from amazon themselves though, with third-party sellers still free to use. Either way it was baffling - Amazon seemed to be trying to incentivize their Prime service by removing the option to buy from them.
Moves like this don't always have the best history. The biggest example of something similar I can think of is when Google tried to get more people to use G+ by making it a requirement for you to have an account in it to comment on Youtube. As someone who spends a lot of time on Youtube I know that the community were vocally against that from the beginning - I haven't made a video comment in years because G+ just complicated the entire process and I didn't want to deal with it. Trying to push a service on people by removing their access to things doesn't always work and often just pisses people off.
Since this happened the block has been removed from listings in the UK store, which suggests either a mistake on their part or a u-turn upon witnessing the reaction from customers. I guess we'll never really know, but if this is an option that Amazon has ready to bring into use I don't see it going well for them...