Now that gnome-user-share has been synced with Debian, the only other remaining really old GNOME component in Ubuntu is vino. vino provided the Desktop Sharing preferences dialog to allow remote desktop access to the local computer. (You can then use an app like Remmina or Vinagre on another computer to view or even control your computer from another computer.)
Ubuntu’s vino is over 4 years old, being stuck at version 3.8 because version 3.10 replaced the Desktop Sharing dialog with an integrated Settings > Sharing panel, but Unity’s System Settings panel never had a Sharing panel because it is a fork of GNOME’s 3.6 version.
vino 3.8 as included in Ubuntu only shows the Desktop Sharing dialog in GNOME and Unity. Therefore, it is not shipped in any other Ubuntu flavor by default (except Kylin but that’s probably accidental since Kylin used to ship Unity). That means this issue really only affects GNOME and Unity.
The Ubuntu Desktop Team would like to update vino now. I am unaware of any equivalent to the Desktop Sharing dialog in other Ubuntu desktops (except Kubuntu).
The Launchpad bug for this issue is LP: #1271358