I never understood why this kind of information is useful (on FB for example indeed). But maybe I am missing the obvious?
What does it matter if an user is online through the web, through their mobile.., or for that matter via their smart TV, their iWatch (or whatever it's being called as from today) or Grannies state of the art flexible kitchen sink with integrated internet? Who cares? The point is that they are online, I don't care from which of the plethora of devices they might use.
I might not see the value clearly, so if someone can enlighten me?
I think it would be really hard to tell if your device should be considered mobile or not.
There too many devices and combinations, as noted by @Grover.
About the facebook example, I believe it indicates if the user is connected by the facebook app or the web interface. I could be wrong though.