My take away from Gobekli Tepe is that there were probably more complex societies and political entities going back to "pre-history". This seems clear from Gobekli Tepe but also sites like Stonehenge.

A really obvious one here is the Bronze Age Tollense Valley in Germany which shows a level of sophistication that does indicate that even though these were tribal societies, they were not the disparate tribal people which we associate with that era. It actually isn't too surprising.

If we look at the Americas at the time of European contact... these people were practically in the stone age yet we see some rather advanced political entities like the Aztec Triple Alliance, the Incan Empire, the Iroquois Confederacy, some weaker tribal coalitions like the Huron-Wendat, the Powhatan, and so on and so forth.

Even archaeologically we can see the development of several pre-Incan states in Peru and the surrounding countries. Cahokia is a really obvious one, as a city in the Mississipi going back centuries. The one that disturbs our perception of these societies and places is the fabled, and now more or less confirmed, ancient cities of the Amazon.

So yes, fabulous megaliths aside, it seems that peoples were organizing, forming villages and cities, abandoning cities, changing from nomads to pastoralists to agrarian societies and vice versa, as well as creating intricate networks and political entities between cities, villages, and tribal peoples.

If Europeans had not documented it, we probably would not know that the Iroquios Confederacy existed as a polity, nor the Comanche or Apache etc. Archaeology would have a hard time proving it. We can assume that this has been the case in the Old World for millennia as well.