The only times I've encountered a game or program not launching via Bottles, it had to do with missing dependencies and/or other issues with the installer.
SteamDB has a list of dependencies that are used for Ape Out, of which you can try adding to your Bottle.
However, I would try running the game in Lutris; In Lutris, if you encounter issues with the game, you can click on "show logs" which will (hopefully) help you out a great deal. Lutris uses their own runtime which is primarily pulled from Valve's Steam runtime (IIRC), saving you from having to hunt for dependencies (if missing dependencies are the issue).
No problem! I'm glad I could help :)
Lutris does not automatically download user-made scripts; you have to add them manually.