This is the most effective fix for the "Failed to Initialize" error. Steam stores old login tokens and API data in a cache. When that cache gets bloated, Absolution can't read it.
Warning: This will log you out of Steam and require you to log back in. You will not lose game saves.
config folder and delete the file htmlcache (or the entire folder if small).By clearing the depot cache, you force Steam to re-authenticate every game in your library, including the specific API key Absolution needs.
If none of the above work, force the game to launch offline:
Hitman: Absolution often fails to initialize properly if Steam lacks permission to write to its own configuration files.