I don’t think you can view this as an admin. The user can view it under their profile in Gainsight > Inbound Emails
As Customer Team Operations we support our Customer Success team with Gainsight Administration needs. The issue is that when a non Ops user clicks that Inbound Email Setting icon they receive an insufficient permissions dialog box. That is why I sparked up the conversation on my ability to reply to an email or chat request with their BCC email address.
I will touch base with our IT Team to see if the SFDC permission restriction is required for some reason to allow the self-service of the team to view their own; seems like this is something an Admin should be able to view/audit/support.
Thanks @john_apple