Stripe is one of my favorite startups with a valuable solution and we use them for our client sites and our own products. To me though they didn't do something that hadn't been done before, what they did do was take a pain in the ass problem and made it stupid easy to solve. I am sure they have some amazing technology especially on the fraud side, likely something that could be called revolutionary, but in the end they started by solving a problem that wasn't new, just painful for everyone.
BTW -- not trying to take anything away from Stripe, but other players were already in the market with payment API's before they started. So in that since they aren't revolutionary in my opinion.