Croteam mentioned that VR is now supported on Linux and Vulkan API is supported and recommended for VR usage. However, "This is waiting for updated SteamVR for Linux to be released. Once that is out, we will enable the Linux download for all owners. Note that this whole system is very early, and there might be problems with stability and performance"
Aside from the Linux work, this Serious Sam VR update also has a wide variety of other improvements too. More details via SteamCommunity.com. Should be exciting once the Linux build and updated SteamVR ship. If there's a benchmark mode, it will be tested on Phoronix.