While I can't readily diagnose your issue, I want to focus on your compatibility version being the demo? So, you downloaded the ZIP file that contains both `TheChoicerVoicer_0-5-3 standard.exe` and `TheChoicerVoicer_0-5-3 compatibility.exe`, and the compatibility one works but says it's the demo, and won't play the game modes for you? I've heard before that people accidentally download the wrong version or have issues with getting the latest update from Itch's UI; while I'm glad compatibility isn't crashing, it's supposed to be the full version of the game.
When you run the compatibility version, does it say it's version 0.5.3 in the top-right of the menu?