Amazon has their own payments solution. I've actually seen it replacing PayPal several places, like buying WiFi on flights.
Hopefully, the industry will shift as more options become available and user-friendly. PayPal has the advantage of name recognition, but Amazon shares the same, and frankly, I personally regard Amazon more positively than PayPal. Hopefully, the industry continues its trend, now a quasi-oligopoly and eventually monopolistic competition.
Like others have mentioned, I too wonder how they are going to divvy shares.