And what about the folder titled "saves" inside it? I guess those are the saves that I have to keep right? They look like the same type of files that the saves for Princess Trainer were. I don't think I have to delete them along the rest of the previous version?
You can delete everything. I'm not sure how it works exactly, but my saves were still there after I deleted the old folder. Just to be sure, run the new update first, before you delete the old one.
Here's a screenshot of my saves:
For the issues with the .exe, try extracting the game again from the archive file. If that doesn't work, re-download the game.
PS: Dude, I'd like to help you, so please use the reply function on the bottom right side of my comment window. It automatically quotes my post and lets me know you're talking to me directly. Otherwise, it clutters all the replies that have happened within a reasonable time frame between each other as one notification and I might ignore you, since I wouldn't know that you're still having an issue.