There is very little connection between these two. Diamond does not claim that there is any connection between types of agriculture and types of government. For example, he does not claim that some kinds of agriculture led to democracy and others led to communism. The only claim that Diamond makes is that agriculture led to complex societies and that the areas that got these things first became dominant in the world. Their forms of government have come to prevail in the world today.
For example, Diamond can help us understand why democracy exists to some extent in countries as far apart as the US, India, South Africa, and Australia. His argument tells us that agriculture arose first in Eurasia and that rise helped Europe to come to dominate the world. Since Europe was able to dominate the world, European countries like Great Britain were able to conquer people across the world and either replace those people with white settlers (as in the US and Australia) or impose their systems of government on the people they conquered (as in India).
However, there is no way to take Diamond's arguments and explain why some countries have developed communist governments and others have become democratic.