Take a look at this link. It seems like there is a process for asking Discord to add a game.
https://support.discordapp.com/hc/en-us/articles/217960107-Games-Detection-101However, there could be a problem with getting Discord to recognize Zero-k. When I followed the instructions that Discord gave in the link above I got the following.
cmdLine:""C:\Program Files (x86)\Steam\steamapps\common\Zero-K\engine\win32\104.0.1-287-gf7b0fcc\spring.exe" --menu "Chobby v1.6.11.4"" |
exePath:"c:/program files (x86)/steam/steamapps/common/zero-k/engine/win32/104.0.1-287-gf7b0fcc/spring.exe" |
Since the path is using the version number my guess is the detection of Zero-k would fail the next time the engine is updated.