Cap your FPS to any number that is a multiple of 60. That can be 60, 120, 180, 240, etc.
Looks like it has to do with cl_engineHZ "60" but this cvar cannot be changed at this moment.

By default re-released Quake uses Vulkan API which is great but Quake itself lacks support for Fullscreen Exclusive mode while using Vulkan and I blame exactly that for microstutters. Yes, Quake in Vulkan renders in borderless fullscreen. Yes, Vulkan actually supports Fullscreen Exclusive mode[www.khronos.org]

You may wish to change used graphics API for now to Direct3D 11 as Quake supports Fullscreen Exclusive mode with it which may help some of you with stuttering.
You can do that by adding following line to games' launch options:


And don't forget to disable fullscreen optimizations on Quake_x64_steam.exe to actually get Fullscreen Exclusive mode.

Hoping for an update that adds Fullscreen Exclusive for Vulkan in Quake Re-release