Tessellation control and evaluation shaders are now supported within Intel's ANV Vulkan driver. Obviously the Intel Mesa OpenGL driver had been supporting tessellation shaders for a while now, but up until now they weren't supported by the company's open-source Vulkan driver.
The .tessellationShader bit was flipped on today with this commit after a lot of earlier work landed to the ANV driver as well as NIR and the SPIR-V code within Mesa.
Other VkPhysicalDeviceFeatures not yet supported by the Intel ANV Vulkan driver include multiDrawIndirect, depthBounds, pipelineStatisticsQuery, shaderStorageImageMultisample, shaderStorageImageReadWithoutFormat, shaderStorageImageWriteWithoutFormat, shaderInt64, shaderInt16, shaderResourceMinLod, variableMultisampleRate, and inheritedQueries. Some of those remaining features are big ticket items, but will hopefully be scratched off the list in time for more Vulkan Linux games arriving later in the year.