There are reports today that those opting into the public beta of Talos Principle are now seeing the Vulkan support exposed as an option, a few days after it was made available to public Windows users. I've been part of a private IHV test beta with Croteam for trying out the Vulkan Linux support, but so far my efforts were hampered by various bugs in both the Intel and NVIDIA Linux driver stacks.
I haven't yet tried today's updates to see if the Vulkan Linux issues have been sorted out for Talos Principle, but will be doing so shortly. If all is well, I will then finally deliver a few GL vs. Vulkan benchmark results on Intel and NVIDIA. Sadly, AMD Linux gamers are still waiting for a public Vulkan driver release.
Update: Testing of my IHV beta is still broken on both Intel Skylake and NVIDIA's Vulkan drivers when switching to Vulkan from OpenGL. Black screen.
Update 2: I have a workaround figured out, will have some OpenGL vs. Vulkan tests up shortly.