I don't doubt it gets better but as long as you can't run DirectX programs on Linux, I don't see it going anywhere. And I doubt there will ever be a good wrapper, not to mention it "costs" you a lot to wrap api calls.
Of course you can play games on Linux but not all and not the important ones (while "important" may be totally subjective, of course).
I agree with that. Even though, with wine, you can play games up to DirectX 9 most of the times without much problems and very little performance lost.
Question is, will DirectX always stay relevant? PS4 doesn't have DirectX and is still getting the games. Vulkan is coming and could very well replace it. Most modern engines already run on linux.
Yeah but how old is DX9? You won't notice the overhead because PCs easily outperform usual DX9 PCs.
Question is, why would DX not stay relevant? Consoles never used a standard DirectX but it still exists. Yes, Vulkan is coming but it has to prove a lot to devs to make them change their mind about the mess that OpenGL currently is. And which modern engines run on linux and get AAA titles? They are compatible with Linux (whatever that exactly means in their respective contexts) but if the games are missing, who cares if they do? If nobody "tests" this you can promise everything :)
I don't see that DirectX will get lost anytime soon because of Linux/SteamOS on the gaming side. Win10 will be free for a lot of people, it will feature DX12 which is a huge step forward for gaming purposes, especially the D3D part.