You are right that the east-west axis is an ultimate cause. On the other two, however, you should put the presence of many suitable wild species of plants and animals in Eurasia and the ability of those plants and animals to spread easily as the other two ultimate causes. You can see this in Figure 4.1 in the book.
The presence of many domesticable species allowed agriculture to start in Eurasia. The east-west axis allowed agriculture to spread. Agriculture, as Diamond explains throughout the book, is the key to creating large and complex civilizations. These civilizations allow “guns, germs, and steel” to arise or be invented.
So, the most ultimate causes are the fact that Eurasia had many domesticable plants and animals and the fact that its long east-west axis made it easy for those species to spread.