Very sorry for the delay.
The log file looks clean. Can you post a log from a failed launch? Same process, start the game and let it fail, and go back into the View -> Log Files. There's a drop down box there to change it to output_log.txt.
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Seems like an interesting issue. There may have been left over changes in their steam folder. If you uninstall through steam, I don't think it removes files that were placed there outside of the game. You may have to manually delete the 7 Days To Die folder, then re-validate in Steam to fix it.