Make sure the bottle that is used matches the arch type of your OS i.e. 64 bit Linux OS should use a 64 bit bottle and run the 64 bit Cheat Engine. Next, CEServer must be downloaded and executed:
Download Page: https://www.cheatengine.org/downloads.php
Navigate to the "Server (For network scanning) section" of the page
Download and extract: Linux x86_64 (Cheat Engine)
Open a terminal and cd into the extracted directory
Run the following command: sudo ./ceserver
Once running, launch Cheat Engine and select File > Open Process > Network and type the following for the IP address: 127.0.0.1
then click connect.
Now all running process will be exposed to cheat engine without the need to run games in the same bottle. You can now use cheat engine as normal. ceserver must be ran prior to running cheat engine.