The described functionality is handled by the Google App Engine Support for PHP plugin. The plugin is no longer maintained and is incompatible with PhpStorm starting from version 2018.1.
With PhpStorm, you can develop a PHP application for running in the Google PHP Runtime Environment. PhpStorm supports all the major Google App Engine for PHP development practices and provides the possibility to run and debug your applications locally before uploading them to the runtime environment.
Google App Engine support in PhpStorm
A dedicated project type with a specific directory structure and configuration file.
A dedicated App Engine for PHP run/debug configuration for running and debugging applications on the PHP Development Server which comes bundled with the Google App Engine for PHP SDK.
Uploading applications using the command of the Tools menu.