How did you get it installed exactly? I download it and extract it, try to run the exe through Bottles but it doesn't seem to do anything.
Never mind, I'm dumb. Literally just had to unzip the game and put all the files in one location. Then open up Steam, click "Add a Game" in the bottom left and navigate to the miniDOOM 2 EXE file. After that right click the miniDOOM 2 listing in Steam and select the Properties option. Click on the Compatibility row shown in my screenshot, and enable "Force the use of a specific Steam Play tool", then select your preferred version of Proton from the drop down below. Huzzah! 