Is SuperSU a "rooting app" or is it an "app that requires root"?

From app's description in Play Store:

SuperSU is the Superuser access management tool....

SuperSU allows for advanced management of Superuser access rights for all the apps on your device that need root. SuperSU has been built from the ground up to counter a number of problems with other Superuser access management tools....

_{(Emphasis mine)}

In more simpler words, it manages whether an app should gain superuser privilege per the settings chosen by the user. It requires a specific su binary, so first, it attempts to gain root access to mount system partition in rw mode, then it attempts to replace the existing su binary with its own binary (an educated guess). This technique sometimes (often in my device) fails so it suggests you to root the device using the recovery mode.

I suppose it should be clear now what that app is about and why does it need root access.

Edit:

You misunderstand the meaning of rooting the device and managing root access to all the apps in the OS. This link takes care of the former (that zip also installs the SuperSU as a system app) while the app takes care of the latter.