Hey Andyj, For this unit you may need to run additional wiring. If there is already a C-Wire (Common) in place you should be able to use this one. If not, then you would need to use the included C-Wire cable that can be configured to go from the G to C terminal at the Control Board.
From your picture though, it does look like you don't have the Common, so if it was working with the Nest, it might in fact work with your setup. Of course that does assume that the G-Wire you have there has been setup like I mentioned with the Cable like what is included with the Honeywell.