Alright. I'm going to give you some step-by-step instructions. Hopefully this works for you:
First things first, have you properly extracted the folder after downloading it? If you don't do that, the game can't properly access the save system because it's still in read-only mode. Make absolutely sure you've extracted the game after downloading it.
If you've done that, the next thing to try is this:
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.
Try running the game again.
If you've tried both of those things and it doesn't work, let us know and we can proceed with next steps.