Although there are many options for how to notify people, the one most reliable mechanism is simply by email. Everyone has an email address and it is the still the most reliable way to reach people.
The share module is simply a form with a list of users (from your graph) where an email can be written and then sent to the selected people from your user list. The email is sent in the background and uses the configured SMTP configuration details provided via the Settings in the studio.
This module useful but more a proof of concept as a way to selectively push notifications to your website users. In future it may be integrated with other messaging networks to provide other ways to share new content.