OK, here's some instructions. Hopefully this helps you out:
First, make sure you still have the zipped Grove MacOS folder you downloaded here from Itch.io. If you deleted it or something you'll want to download it again I'm afraid...
Next, you want to make a new folder. Call it whatever you want, and you can move this wherever you want later.
Open the zipped Grove file you downloaded.
Open the new folder you just created.
Click and drag ALL of the contents from the Grove download to your new folder. Then try running the game again.
If that doesn't work, next try unarchiving the zipped folder (navigate to the newly downloaded Grove file in the Finder app and double-click on the ZIP file. After several seconds, the file or the folder should decompress and 'unarchive' right there.)
And then, using Finder, move the Grove application to the dedicated Applications folder.
Hopefully this works for you!