In Chapter 3 of Guns, Germs, and Steel, Diamond is trying to explain to us why Pizarro and his Spanish soldiers were able to defeat the Incas even though they were badly outnumbered. He wants to establish the idea that “guns, germs, and steel” were the factors that allowed the Spanish to win. The best way to explain this is through anecdotes. There is no other good way to do it.
In particular, let us think about the use of statistics. Let us try to imagine what statistics Diamond could possibly deploy that would prove his point. Let us also think about what statistics are even available. One point that Diamond is trying to make is that the smallpox epidemic helped defeat the Incas. Imagine that Diamond wanted to say how many Incas were killed. There were no censuses at the time and so there is no way to know how many Incas died in the epidemic. Even if Diamond could tell us, what good would that do? There is no way to present a statistic to prove that smallpox helped the Spanish win.
I would argue, then, that Diamond uses anecdotes in Chapter 3 largely because A) few statistics are available and B) statistics would not really prove his point any more effectively than anecdotes do.