I'm not sure how much you are following, but AMD is doing quite well on Linux/*BSDs (at least regarding graphics, but they haven't had any interesting CPUs for a while). Mesa 17 has just hit OpenGL 4.5 compatibility on last 4 generations of Radeons [1].
Radv, community-developed Vulkan driver supporting last 3 generations of Radeons, supports vkQuake, Dota 2, and The Talos Principle, which is pretty much everything there is on Linux [2]. Playing Doom 2016 over Wine using Vulkan is also working if one uses airlied's branch [3]. Performance is not on par with Windows right now, but I expect it to improve over time.