At the moment if I have a chatroom full-screened inside a browser tab, my tab gets updated with an unread message count:
In User Preferences > Chat, there’s an option that allows a user to define granular rules for an “activity indicator in header” for the Chat plugin.
Right now, the unread count in the browser tab doesn’t reflect my choice for this setting, i.e. I can choose “never” and still get a count that increments for every unread message in the chatroom.
My guess is that activity indicator in header is referring to the little bubble you get on the chat icon itself:
and in that sense I’m pretty sure that the setting is technically working as intended.
That being said, my guess would be that a user digging into their preferences to define a rule for an “activity indicator” is probably hoping to hit the counter in the browser tab too, considering that’s a relatively high-visibility way that the Chat plugin indicates activity.