I'm also reporting the same issue. idk if there is something I'm missing but my config is Arch Linux. It neither works in the itch app or manually through the console.
This is what I get in my logs
./tc2.sh
[S_API] SteamAPI_Init(): Loaded '/home/isaac/.local/share/Steam/linux64/steamclient.so' OK.
Setting breakpad minidump AppID = 243750
SteamInternal_SetMinidumpSteamID: Caching Steam ID: 76561198142142680 [API loaded no]
[Source Mod Launcher] Launching default game: tc2
And then the program exits, either when launching it through script or directly from the executable.