Only System Administrator Users have the ability to Enable or Disable the drag-and-drop feature on the full Staff Calendar.
To modify this setting, navigate to the Settings Tab (available from the + All Tabs page).
Select the 'Advanced' Tab.
Look for the Checkbox labeled: "Enable Calendar Drag and Drop"
Here you will check the box (set the value to True) to Enable drag and drop OR,
Uncheck the box (set the value to False) to Disable drag and drop.