If you click the Install button and start the installation, it should recognize that the game is there. From there it might install a small update and let you play.
This is assuming that the default install locations setup in the Game Install/Update section of the Blizzard app settings are set to the same location the games are installed to. If not set properly, you may run into a scenario where the game gets reinstalled into a different folder or into the pre-existing game folder.
As an example, if you have a World of Warcraft folder in C:\Program Files (x86), the default install location should be set to C:\Program Files (x86).