You have to run the uninstaller to remove the application, there is more to the program than just it's program files. The uninstaller is still found in the place it always has been (Control Panel > Programs and Features on Windows and Applications/Utilities/Adobe Installers on Mac).
If you just want to install an application over the top of itself, go to the Creative Cloud desktop app, select the Apps tab, go to the Find New Apps section and click the drop-down menu (Filters and Versions) and choose Previous version. Find the application you want to reinstall on the list, click the Install button and select the version.