The answer to this question can be found in Chapter 3 of Guns, Germs, and Steel. In that chapter, Diamond describes how the Spanish conquistadors were able to defeat the Incas at Cajamarca. He lists and discusses a number of factors that allowed this to happen. He begins his discussion of writing on p. 78.
Diamond says that writing was important because it could transmit information more effectively than word of mouth could. It could be more accurate and more detailed in transmitting the information and it could spread the information farther. Because the Spanish had writing, information about Columbus’s voyages reached Spain quickly and was disseminated, making more Spaniards want to come to the New World and giving them instructions about how to do so.
By contrast, the Inca emperor did not know much about the Spaniards at all. He only got a few verbal reports about them and therefore did not know how many of them there were, how much military power they had, and what they were intending to do. If the Incas or the other native people had had writing, they would have been able to spread information about how the Spanish had behaved in the Caribbean and elsewhere and the Incas would have been more on their guard.
Thus, writing is related to conquest because it gave the Spanish conquistadors a great deal of information that helped them reach the Americas and helped them defeat the Incas.