What is difference between the kingdom of Gilgamesh and Cyrus the Great's kingdom in regards to the ideas of Chapter 14 of Guns, Germs, and Steel?
I am slightly confused by this question because, in fact, neither Gilgamesh nor Cyrus the Great is actually mentioned in Chapter Fourteen of this great book. The main idea of this chapter is the way in which some societies developed from being hunter-gathers to becoming sedentary and developing in food production and in other areas, which gave them the distinct advantage over other societies, which in turn led to their dominance and the formation of civilisations and empires. However, this chapter also looks at the different "chains of causation" that resulted in different "proximate agents of conquest" based on the varying roles that germs, writing, technology and centralised political organisation played. Diamond gives an example of how this process was different for different societies:
An empire arose without writing among the Incas, and writing with few epidemic diseases among the Aztecs... Among the dozens of Zulu chiefdoms the Mtetwa chiefdom enjoyed no advantage whatsoever of technology, writing, or germs over the other chiefdoms, which it nevertheless succeeded in defeating. Its advantage lay solely in the spheres of government and ideology.
What is key to realise therefore is the way that different societies developed and managed to dominate the peoples around them through a standard "chain of causation" that involved a list of "proximate factors" that are different in the case of each society. Diamond's book does not talk about the two examples that you refer to, but you might like to take this further and examine the "proximate factors" that were responsible for these two kingdoms' rise to power.