It appears that the "notifications" tab has been rolled out for all sites, similar to how the regular inbox is. From the blog post announcement:
Notifications are now:
- global: get a badge on Stack Overflow and you’ll see the notice on Gaming
Can the notifications tab be added to chat's global inbox? (Not inside an actual chat room, mind you, where there is no inbox at all, but in http://chat.stackexchange.com/ for example, where there is).
Here's some screenshots to illustrate the issue:
For comparison, the dropdown usually looks like this:
Note that "email settings" is also missing from the box on http://chat.stackexchange.com/. My guess is that we are looking at an outdated version of the "global" inbox on that page.