The kernel driver manages things like display setup, memory management (isolation between processes), and funneling of commands from user space to the hardware. This is more a replacement for Nouveau than NVK.

NVK generates the commands to send to the hardware, by converting vulkan APIs to Nvidia-specific instructions, and feeds them to the kernel driver.

This new driver (along with the modules Nvidia have released as OSS [1]) are kernel drivers and do not break userspace. NVK is a Vulkan implementation for Nvidia GPUs as part of the Mesa project (the same project that AMD's userspace drivers are a part of, even though AMDs kernel drivers are in tree). They are both needed to make a cohesive driver.

[1] https://github.com/NVIDIA/open-gpu-kernel-modules