"non-privileged users" are "normal" users, such as students.
Privileged users could be teachers, managers, admin... depending on how roles (and rights on capabilities) are defined on your site.
I understand it as an attempt to use some general expression. Because it is not correct to say "teachers" - depending on the roles configuration on the site, teachers may or may not have such privilege. So "non-privileged users" means anybody who were not given explicit privilege (right, permission) to view email addresses.