https://www.reddit.com/r/SteamDeck/comments/15tk0u7/black_ops_3_boiii_client_install_guide/

https://www.youtube.com/watch?v=AxDttxwpcmc&t=116s

Using the unofficial boiii client fixes Black Ops III (Black Ops 3 for people searching on Reddit for a fix) on SteamOS 3.5.5. I was able to play a match of zombies with no issue. Tested with mods and splitscreen. Everything worked. No crash going back to the menu either. Only three drawbacks:

  1. There’s a watermark in the top left corner. A small price to pay to finally get the game working again
  2. Game takes a long time to boot. Like a good minute or so. Once it’s booted, it’s all good.
  3. Online play may not be safe. So only use this workaround for offline or splitscreen. If you add a steam_api.txt file to the game folder, you can access Remote Play Together. Inside the text file should just be a single line with the game’s appid.

You can follow either linked guide. It’s a very simple install process. Just an exe file and two folders.