We first heard about the story on AndroidPolice.
Of course, there are some strict guidelines to follow in order to qualify for the full $5,000 per app.
Basically, Amazon is ensuring that its new 3D "Dynamic Perspective" feature will be used to some extent in the app, which would help the feature from falling into gimmicky obscurity. Dynamic Perspective is a bit similar to the parallax feature on iPhones, but it takes things to another level by using the Fire Phone's extra cameras to add 3D depth to apps and home screens, so that things shift and react to your movements.
Other than that, Amazon is also requiring apps to integrate with its multitasking user interface "Carousel" to keep browsing between different apps cohesive.
Why is Amazon offering developers essentially free money?
It's important to remember that Amazon is entering the smartphone market at a time where fragmentation is at an all time high. This trend can increase the workload for developers seeking to offer their app on as many platforms as possible, an issue Android has run into into in the past, and Apple could face if it continues to expand its iPhone product line.