Let me help you with this.
I first want to thank you for posting these questions here because there are many other customers with this queries and I am sure it will be very helpful.
As you mentioned, the latest driver we have has a Control Panel with a new view but this control panel has been included on the drivers from other older versions. When you install the driver it creates a short cut in the desktop but you can also access it by right clicking on the desktop or from Control Panel so if you would like to delete the short cut you can do it and it will not cause any problem.
I must say that the icon tray for Intel® HD graphics Control Panel provides three options only which are: Graphics Properties, Graphics Options, Exit tray but the last one Intel® HD Graphics Control panel is gray out because is just the name of the icon so it is not an option meaning it is expected and working normally.
I hope this helps.