Windows 8.1 update 1 didn't remove the desktop app from the metro screen, so it's likely that someone else had done it (you should be able to find the desktop app in the all programs section so you can pin it back on the start screen).
As said, desktop was not removed in any update. Nor was split screen. You can not keen remove the desktop icon, from all app screen. So something your end is very broken.
Actually Desktop tile shown at Start Screen is a special type of shortcut which is present in "Programs" folder and if the shortcut gets deleted from the folder, it also disappears from Start Screen and you'll not find it in "All Apps" page as well.
Desktop_Shortcut_Missing_Programs_Folder.png
To restore Desktop tile at Start Screen, you just need to copy Desktop shortcut in "Programs" folder again and it'll reappear at Start Screen.
dunno where it went but heres how to put it back
http://winaero.com/blog/fix-desktop-tile-is-missing-on-the-start-screen-in-windows-8-1/