I'm actually working through a similar issue right now as well elsewhere in the forum.
That window is looking for a CUDA supported video card. Not sure if your AMD supports that but I've found that it may not even be that important. Turns out GPU has very little to do with AE. The GPU accelerates the ray-trace engine which apparently isn't really good for much anymore. (If you go to comp settings -> advanced and switch it over to ray-trace you'll see how much you lose to utilize the GPU)
Here's a somewhat related thread discussing those GPU concerns. Nvidia GTX 780 Ti or GTX 980 (AE CS6)
Here's another thread that talks about the CPU/hardware issues that may find are more your issue. Re: AE only using 25 percent of my CPU
I don't have an answer unfortunately. But hopefully a little bit of this research is helpful.
AE uses the GPU for very little. See this page: GPU (CUDA, OpenGL) features in After Effects
Basically, the only thing AE uses it for is the obsolete ray-traced renderer. The ray-traced renderer relied on CUDA technology from NVIDIA. It was only accelerated on certain NVIDIA cards. An AMD card will never work with the ray-traced renderer, but that's okay because very few people use the ray-traced renderer! Instead, use Cinema 4D which comes free with AE or use a third-party plugin like Element or 3d Invigorator (both of which can use AMD cards).