With there being vkQuake for implementing Vulkan for the original Quake (id Tech) engine, the latest is now getting the Unreal Engine (1) from the end of the 90's working atop this modern Khronos graphics API. This nearly 20 year old game engine was first designed for using the Glide API and only later added OpenGL and Direct3D support. So now this game engine that powers the legendary Unreal and Unreal Tournament games could soon be full-functioning on Vulkan.
This effort is unrelated to Epic Games' work on supporting Vulkan with their modern Unreal Engine 4. Rather, this Vulkan renderer for Unreal Engine 1 is being worked on by Russian developer Roman Zavalov.
Besides Unreal and Unreal Tournament, there are also Unreal Engine 1 headers and library support for Rune and Deus Ex too.
The code for this in-progress Vulkan support can be found via this GitHub repository. There isn't yet Linux build support integrated, but with the code being out there and public, it probably won't be too long before we see it advancing for Linux gamers wishing to relive these classic games atop Vulkan.