I believe this is a case of needing to extract the game files first, not running it directly from the archive
There should be some tutorials laying around on the internet... but I think you can just make a new folder on the desktop (call it 'GroveGame', or something along those lines), then open the original downloaded archive until you see the 'Game.app' file and the 'credits.html' file. Drag those out of the archive folder, and put it into your newly created 'GroveGame' folder
I don't think MacOS can edit files when they're archived, hence the need to extract them first and the 'read-only' mention in the error message! Let us know if the above solution works out for you.