Reading the grid, the bold section seems to be in error, as if I close any App I end up back at the start screen. The desktop is an App in Windows 8.x
Have you rebooted since turning off Sync? Do you have a local profile to test?
Yes and Yes.
Also, I think the section in bold under "After 8.1 Update" reads like this to me:
Tablet
Boots to start Screen (check)
Closing app takes user to desktop (current behaviour - this is what I find odd))
Pics, Music and videos open in Modern App (check)
Non Tablet
Boots to Start Desktop (check - but I have unchecked that box under Taskbar etc. So, I boot to Start Screen)
Closing all apps takes user to desktop (check - this is what I find odd)
Pics, Music and videos open in Modern App (check)
Notice though that in that matrix that you provided - under tablet, when closing all apps, it does not say actually what happens - when technically, they should have said reverts to Start Screen (or desktop, if they have changed it, which I doubt it as it does not make any sense - except for those using the Surface Pro or equivalent). You see what I mean?