I am inclined to think that of the 6 primary characteristics of a state, intensive agriculture is one of the most important. It allows for the other 5 characteristics to happen. Intensive agriculture leads to finding ways to increase the carrying capacity of the land, and allows for less people to be involved in food production leaving them open for specialization. With extra food and swanky new luxury goods made possible by specialization, the state can trade with other states for their products building a complex economy. This complex economy then gives rise to marked social stratification. With extra income and a competitive market, some people are bound to make more money and have more excess than others. This marked social stratification either creates or enforces the authority of the state. With the complex economy and a shift in focus from food production to other occupations, people naturally flock to a central location more suitable than the country for trading. This creates a dense urban population.
Two of the four classic theories for the development of Ancient States involve intensive agriculture. One theory hypothesizes that irrigation (a technique of intensive agriculture) is what allows for the development of an ancient state because carrying capacity of the land is increased and more food can support a denser population. However, this turns into an chicken and the egg argument when considering the theory that warfare caused by reaching or surpassing carrying capacity developed leaders and is the cause of the formation of a state. Carrying capacity may be increased by intensive agriculture but it attracts a denser population which could lead to warfare over new lands which will then use intensive agriculture to increase the carrying capacity of those new lands and it could go on until the state’s inevitable collapse. Or, lands could be conquered by warfare which then develops into a state. The leaders created have time to figure out better ways to use the land and so they develop intensive agriculture and it goes on until the inevitable collapse. Either way, intensive agriculture is present.
Another theory states that agricultural diversity leads to long distance trade. One state might have something that another state needs. They both use intensive agriculture to get the most out of their land and use that for trading. V. Gordon Childe believed that urbanism led to the development of the ancient state. That this dense population has enough people that they can start specializing. I doubt you could support such a population without intensive agriculture, however.
For all these reasons, I think that intensive agriculture is probably one of the most important characteristics of an ancient state. I don’t think it is required, I know it isn’t required but it seems to be a pretty common practice among ancient states. States have even collapsed over a bad harvest. We don’t really need writing, but everyone always needs food.