I'm not sure what happened. If I had to make a guess, I'd say that it wasn't just an icon you had on your desktop, but your coollection file itself.
Your coollection file contains all your personal data:https://www.coollector.com/help.html#coollection
But don't worry, the app creates backups automatically:https://www.coollector.com/help.html#backups
The help file will help you locate the folder "Backups". It should be filled with lots of .cool files. Use the date to find the latest backup, copy it to your desktop, give it a simpler name and voila, you can click it as you were used to.