After installing project_zomboid_41_77_hotfix_59328.sh I get the following:

$ ./start.sh
Running Project Zomboid
64-bit java detected
Picked up _JAVA_OPTIONS: -Dawt.useSystemAAFontSettings=on
Picked up _JAVA_OPTIONS:
[S_API] SteamAPI_Init(): SteamAPI_IsSteamRunning() did not locate a running instance of Steam.
[S_API] SteamAPI_Init(): Loaded '/home/eugene/.local/share/Steam/linux64/steamclient.so' OK.
[S_API FAIL] SteamAPI_Init() failed; create pipe failed.Message: 'Fatal Error', Detail: 'Steam must be running to play this game (SteamAPI_Init() failed).
'

And then the game crashes to the desktop. It looks like something went wrong.

To make the game not require Steam, edit the file game/projectzomboid/ProjectZomboid64.json, change there
"-Dzomboid.steam=1"
to
"-Dzomboid.steam=0"

Fixed in project_zomboid_41_77_hotfix_59340.sh.