In a post on Hacker News, MyOwnClone explains that he built the port on top of existing ports for iOS and Mac, with lots of tweaks to get it to work within the watchOS framework. It runs at 60 frames per second with a 640x480 resolution, and it can run at a higher resolution with a lower framerate.
The port is available on GitHub, with a demonstration and more information on the build process available on YouTube. Installing the game on an Apple Watch will require code compiling with a Mac, Xcode, and the copyrighted Quake assets.