The person who creates the event is not the person requiring the notifications of registrations. How to setup emails going to not the site admin or person creating the event online but the person running the event who needs to know who is attending.
By default Event Espresso would use the email address of the user account set as the author of the event for the ‘Event Admin’ emails.
So do the people who will be running your events have a WP User account on the site? If so you could set them as the event author and the emails will automatically go to them without additional changes.
If not, the other option for this is to create custom ‘Registration Approved’ message templates for these people, hardcode the ‘To’ field to be the email address for the ‘person’ the email is intended for and then set that template on the event.
If the latter is the option you prefer here I can add more details on how to set that up.