I should also mention that even on Windows the binary doesn't run quite right. Usually, the first time I launch the game after starting Steam, it crashes; if I start it a second time it runs OK; but at the end of my gaming session when I exit the game from the main menu, Windows gives me an error message "CDE.exe has crashed" so it looks like it's not exiting cleanly.
There's a minor sound issue where the sound gradually becomes garbled over time, but it doesn't start until the game has been running for several hours. Other games have had audio problems with Proton which were fixed by a recent update, but I didn't try CoaDE before that update. Maybe it's trying to use alsa instead of pulseaudio, which has always been problematic for wine on my machine.