I don’t have any idea about your hardware issues. They’re likely unrelated if the game has already been played without issue.
For the steam diagnosing, start with running steam from your terminal, by running steam. You may get lucky and the error is clearly identified in the console.
If that fails, backup $HOME/.local/share/Steam/steamapps/compatdata/221100 - the 221100 is the app ID of of DayZ on the steam store. After backing it up, delete the original 221100 directory and re-launch the game. This doesn’t delete the game, but rather deletes the Proton prefix for the game.
If the game launches, copy any save files (if any) you may have in the backed-up 221100 directory over to the new one.
The above worked for me when I had similar issues when playing Batman: Arkham Asylum.
To be thorough, have you tried any other games to rule out your hardware being an issue?