We are unable to find this option anywhere in the Events Booking ->Configuration area to permit selected users to view / download registrants fro the front end.
You can go to Events Booking->Configuration, click on Options button in the toolbar, find the group you want to be able to manage registrants from front-end, set "Front-end Registrants Managemen" permission to Allowed and users from that group will be able to manage registrants from front-end.