As I said, AFAIK you have everything set correctly. When I was running XenForo 1.5 I had the approval queue link on my site (and for security my account was only set as an Admin, not a Super Admin).
This old thread discussed user approval
https://xenforo.com/community/threads/permission-to-approve-users-is-it-only-for-super-admins.81763/
There's no mention there at all about any separate factors for controlling the counter. So there must be some other factor in play if you aren't seeing the queue counter for one Admin account but are for the Super Admin account. I'm assuming that the user waiting approval was added to the queue after the Admin (who can't see the counter) was given the manage users permission?