Hello - Uncheck ‘Auto arrange icons’ in the context menu > View… any better?
-Pascal
I think the difference is the Rhino desktop shortcut was created as an Admin and is installed in Windows as an All User application.
The other icons you’re moving are folder shortcuts, tied to and unique to your User account.
If you created another user account, the Desktop would show the Rhino shortcut but not the folder icons.
That’s my theory anyway.
I’ll have to check, bu both Rhino shortcuts are created for the user. Difference is the arguments. The one that acts crazy was created during the last update. The stationary one has inside arguments to launch without splash and to launch grasshopper.
Assuming what you say is true. Why is it that when moving crazy shortcut horizontally and if below it, there is the other rhino shortcut. Both shortcuts are moved together? Crazy 
The complexity and vagaries of Windows have always remained beyond my grasp.
At best, I cope with them.