Cannot uninstall Illustrator because CC shows it as not installed

I currently have Photoshop, Illustrator and Dimension installed, and I wanted to uninstall (and reinstall) Illustrator. But when I opened the CC Client, it doesn't show Illustrator or any App as installed - it should say "open" next to the installed app but it says "install". And the drop-down where I wanted to pick "uninstall" just says "other versions".

I do have the uninstall files in my application folder, but I don't understand why I can't do it through the CC App?

I also have PS installed and just to see what's happening I clicked on "install" and it actually started installing Photoshop, even though I've literally used it minutes before (I've immediatly cancelled the installation).