Wow, that is odd. Never seen anything like that before.
Do the Zone Controls & Gear icon show up in other Windows like the Key Editor (they should)?
Right clicking like you did behaves the same as clicking the Gear icon. If you right-click is the item Windows Zone Controls checked so they are visible? If so the only thing I can think of is that you are not seeing them because you have more items selected to display than can be physically shown. Try setting a bunch of items to not display and see if the missing items show up. Also in the right-click list there is an item named Right Divider. Hover over the Toolbar where the divider is supposed to be and it should become visible while hovering. Drag it to the left so there is more room for items to the right of the divider.