I think any registry tool can clear out broken entries like that, and so can dedicated uninstaller tools like Revo Uninstaller Pro (which has a free version).
I strongly recommend making a full system backup in case something goes wrong, and once that's done you may even want to fully uninstall all Cyberlink entries shown in the Windows Apps & features list then install the App Manager and reinstall everything again.
None of this explains how or why things ended up the way they did on your system, but it does provide a way to get everthing straightened out now. You may also want to contact CL
tech support as they may have specific steps to take.