I had the same exact issue (on the same exact Linux distro version) and found this comment on another thread: No Linux support yet? - #88 by Kim_Eik
You may want to check the GitHub project mentioned there in order to find out how to fix the issue:
https://github.com/netbrain/dockerfiles/tree/master/zwift
More specifically, look at the content of this file:
https://github.com/netbrain/dockerfiles/blob/master/zwift/entrypoint.sh
Where it says:
echo “workaround crash issue 1.21”
Look for a couple of commands after that line - those basically install the required dependencies to prevent the app from crashing. You can run those manually with the correct WINEPREFIX env variable set (i.e. pointing to your Zwift installation folder).
That fixed it for me. Hope it helps you too.