Hi,
Messages is built on iChat (or rather was).
iChat could, from iChat 2 video chat within the app itself without resorting to outside apps (using the AIM and from iChat 3, the Jabber accounts).
Screen Sharing was also possible when it used an Audio Only chat with a VNC connection along side.
It used Apple Remote Desktop's engine to this.
Initially this was all the first version of Messages could do but that has then become Video Chat by Invoking FaceTime which expanded into Audio Only chats as that was added the the iOS version.
At Yosemite, Screen Sharing by invoking the Screen Sharing app (Which is part of Apple Remote Desktop !!??!!!) was started.
At Messages 10 (Sierra) all In-app means of Video and Audio Only chat has finished.
The Video Menu has gone and so has the Video and Audio Preferences.
Therefore someone using an older version of Messages will have more in the Preferences and is likely to have the Video menu.
If you have other services like AIM and Jabber or Yahoo plus enabling Bonjour as accounts in Messages then the General Pane is longer.

In the Mac Firewall, which I have On, I have both the Screen Sharing (in System Preferences > Sharing) showing and Messages.


8:00 pm Tuesday; September 27, 2016
iMac 2.5Ghz i5 2011 (El Capitan)
G4/1GhzDual MDD (Leopard 10.5.8)
MacBookPro 2Gb (Snow Leopard 10.6.8)
Mac OS X (10.6.8),
iPhone and an iPad (2)