From the description for Global Group Moderators :
Select which roles can moderate all groups for your site. Global Group Moderators can create groups, approve new groups, remove groups, mange group membership and group settings.

I believe I have updated the documentation, as when I wrote that initially I was confused about the function of Global Group Moderators.

Global Group Moderators main role is to approve groups, when group creation moderation is enabled.

Users in the Global Group Moderators role will receive a private message with options to approve or deny the group, when a group is created.

They are not group admins.