The extension GoogleAPIClient is pretty useless, now that google supports composer for installing the dependency. Another (better and easier for update) way to install the dependency would be:
Adding the api library to composer's json file
An extension, that requires the api client for it to work, can name the dependency in the require field of it's composer.json (which is currently the preffered way as described on the github page). Having a composer.json will also simplify the installation for third party users. ExtensionDistirbutor will build release tarballs including composer dependencies.