To provide further counter-examples, classic Maya polities are frequently considered city-states and functioned similarly to those of Italy and ancient Greece. Several South American societies likewise tended to the city-state ideal as opposed to the single state.

The entire Maya region was made up of competeting city-states. In the Classic period the two largest centers were Tikal and Calakmul and smaller city-states tended to gravitate these two, but not all. Shortly after Calakmul gained the upper hand and defeated Tikal is when the Maya region experienced the Lowland abandonment. It is not entirely clear as to why the area was abandoned. It could be political instability as Calakmul's alliances break down. It could be a result of disease and famine brought on my drought. It could also have been shifting economic patterns as trade routes along the coast became more common and easier than over land. Whatever factor or factors that lead to the Lowland abandonment is still the subject of intense debate. Despite the abandonment the Maya continued to live in city-states in the northern part of the Yucatan and the Guatemalan Highlands up until and well after Spanish contact. The last Maya city-state, Nojpeten, fell to the Spanish in 1697.

Your basic assumption is wrong. In the present, see: Singapore, Hong Kong, Macau... All over Asian in ancient times.

As has been pointed out there's a small problem with the question. Like /u/Rumy73 pointed out, there were city states in the East, ignoring Singapore for the time being.

In fact it's Western colonialism/imperialism that can be pointed out as the cause of their demise in places like SE Asia where they were the dominant "international" political organisation at least for a few centuries.

In Southeast Asia, from the 4th-8th century or so, there was the Muang system. These were spread around the region covering most of SE Asia as well as parts of China and Assam. The muangs in their most typical form were independent walled cities with single rulers. They existed in an extended tribute network with each other and more distant powers.

A History of Thailand by Baker & Phongpaichit has a decent overview put into geographical context that you're not going to get from Wikipedia.

In addition to the other examples provided in this thread, the Swahili cities are frequently considered city-states.

Additionally, the Hausa cities of northern Nigeria are sometimes categorized in the city-state model, prior to the Fulani jihad that established the federated Sokoto Caliphate.

For decent works of comparative history that look at City-states in a Western and non-western context, you might check out A Comparative study of Thirty City-State Cultures and the supplemental Comparative Study of Six City-state cultures, both edited by Mogen Herman Hansen

The east had lots of city states, especially along the Silk Road through Sogdai. They simply appear and peak much earlier, and have histories recorded in non-English languages so are more rarely known.

Bukhara, Samarkand, and Tashkent were all very large and powerful city states. 'The Empire of the Steppes' by Rene Grousset is a good introductory text on the subject.