It doesn't seem to run for me on Catalina. :(
The application “Hamster All-Stars_v1.0.0” can’t be opened.
Here's an important question. Does the app has a no symbol (the O with a slash through it) over the icon? If it does then it is not compatible. If not there's a problem with the application file. Enter the terminal and use the cd command to navigate to the folder with the application. Then do
chmod +x /"Hamster All-Stars_v1.0.0.app"/Contents/MacOS/"Hamster All-Stars_v1.0.0.app"
(I think, I don't own the game yet so I can't check this) and if this doesn't work add sudo to the start. (Note: this could mess stuff up so I'd advise you know a bit about using the console)
Update: Now that I've gotten the game, I can tell you with some certainty that the issue was the application file not being the mac equivalent to an executable and the command should be (after you've navigated to the folder containing the application file)
chmod +x /"Hamster All-Stars_v1.0.0.app"/Contents/MacOS/"Hamster All-Stars"
Note: it is quite dangerous to just run terminal commands given by random people on the internet.
I got it to work on Mojave using this trick but now that I'm on Monterey the terminal keeps telling me:
chmod: /Hamster All-Stars_v1.0.0.app/Contents/MacOS/Hamster All-Stars: No such file or directory
I confirmed I was in the right directory using ls and the app was listed. This happens in both bash and zsh, whether or not I use sudo, before and after restarting. Any clue as to what is going on? When I searched for "chmod no such file or directory" I got an Apple Support thread about admin setup on a powerbook G4.
Update: The Steam version works with no extra work even though Steam thinks its a 32bit game. Weird.