Well AMD will have to keep writing good Linux drivers which will most likely benefit everyone with an AMD card. They're also partnered with Unity and Epic Games which means these engines will make it easier to target Linux as the release platform and maybe port some DX-only features over to Vulkan.
Which doesn't mean any of those changes will be contributed back to upstream, just like it happened with many of the PS 4 features in clang and AMD drivers, where only what wasn't business critical from Sony's point of view was contributed back.