First of all, we should note that Diamond does not simply quote a six-page block of text from some source. Instead, he "weaves together" excerpts from the accounts of various Spanish conquistadors.
But that does not tell us why he did this. It may be in part because he is not a trained historian. Diamond was a microbiologist and not a historian and might not have felt comfortable writing history.
It is more likely, though, that Diamond had a better reason for this. I would argue that he wants to portray just how easily the Spanish defeated the Incas. In the accounts that he uses, the Spaniards' confidence and arrogance shines through. It seems, from these accounts, that they simply could not lose and that they had an easy time of the battle.
This is a good way for Diamond to set up the rest of the chapter. When we see how easily the Spanish won, we wonder how that could happen. That leads perfectly into Diamond's discussion of the advantages that the Spanish had.