The purpose of this module is very different from the of the Libraries API module. This module allows an admin user to both enable JS libraries shipped with Drupal core (i.e. cause them to load on every page), or to link in external libraries via URLs, or upload new JS libraries or scripts that use the core or external libraries.
This is a tool for site builders who don't want to write a module or figure out how to add JS via their theme, or who cannot add custom module or theme code to their site (e.g. Drupal Gardens). It makes it easier for a site builder to add and manage custom JS without e.g. pasting it in a block.