Everyone that has access to Workbench can use Record and Playback.
i'm not the admin of the server, but one of the users that was created gives the following message when I try and start the feature.
'you must possess the 'Process Recording Read/Delete.' permissiosn in order to....'
I was looking for a reference to the list of permissions in LC. I did not see if in the docs.
Make sure the users have "Application Administrator" role. This role contains the Process Recording Read/Delete permission.
What role(s) are you giving your users to grant them access to Workbench?