The true answer to this question is not really found in Chapter 4. Chapter 4 outlines for us the reasons why food production leads to things like empires, literacy and steel weapons. However, he does not tell us why these things developed in Eurasia rather than elsewhere.
The answer to this is that Eurasia was geographically luckier. We can see this in such places as Chapters 8-10. There, we are told why food production arose earlier in Eurasia and why it spread across that land mass.
Essentially, Eurasia had more domesticable plant and animal species. This made it much easier for Eurasians to domesticate those species and start producing food. Once any population of Eurasians did this, their techniques and crops could spread easily because Eurasia has a long east-west axis with few barriers to the spread of crops.
Because of these things, Eurasians got agriculture before other people. This allowed them to have higher population densities, leading to the creation of empires, to literacy, and to steel weapons.