You mean you used the itch app to download it, rather than the website? I guess the app doesn't give you the choice of which version to use, I will look into that with itch themselves. You can try downloading the 32bit version direct from the website, which definitely does give you the choice. Ultimately if you can't get it to work then of course you can have a refund. Details for both options are below:
To try downloading from the website:
1. Use Chrome/Firefox and go to https://itch.io/
2. Make sure you are logged in with your itch username
3. Click the arrow by your profile name in the top right of the screen
4. Select 'My Library'
5. You will see a list of all the games you own, find Cherry Creek and press the 'Download' button
6. You should see a 64bit and 32bit version of the game, you can download and try both
7. If neither work then it may be something
For refund:
1. Email the itch support address on support@itch.io
2. We cannot give you a refund directly so you will need to use that email
3. Let them know the issue, and point to this thread as confirmation if needed