Göbekli Tepe was built ~11,500 years ago, and it probably isn't a coincidence that early agriculture was developed in the same area -- about 1,000 years later. The early agriculture reference that you mention concerns the fact that the was abandoned as early agriculture started to take hold:
> Around the beginning of the 8th millennium BCE Göbekli Tepe ("Potbelly Hill") lost its importance. The advent of agriculture and animal husbandry brought new realities to human life in the area, and the "Stone-age zoo" (Schmidt's phrase applied particularly to Layer III, Enclosure D) apparently lost whatever significance it had had for the region's older, foraging communities.
I haven't seen any sources citing evidence for Göbekli Tepe post-dating agriculture, but there are many lines of evidence that it pre-dates it -- such as an absence of cultivated grains, granary structures, or other evidence that one sees as agriculture actually gets going. All the plant remains that have been found are wild varieties. Thus the mainstream assumption is that Göbekli Tepe was built by hunter-gatherers.
Perhaps I am going too far with my speculation, but GT strikes me on two aspects as being highly unusual, with regard to what I "know"[1] about hunter-gatherer societies.
1. The site seems to be built with a plan. Maybe they did not use paper and pencil, maybe they were using some kind of sand table[2]. And there was a number of people involved, who were quite good at stone cutting, and on a large scale. Just have a look at central obelisk and pedestal [3] - those sharp edges, those smooth surfaces. Now, getting good at something requires daily practice, for a long period of time during which one would rather not go around for hunting. So not only there was a population of proto-carpenters but also societal structure to support them, at least for times of learning and construction work.
2. Even more unusual, the site seems to have been abandoned (evacuated?) in planned manner. Great effort has been made to cover it up with huge mass of soil mixed up with broken stones, as if to make it tougher against elements. This, for me, really stands out. AFAIK the norm is, when supporting culture "loses interest" in site maintainance (like, when all its members are dead), the site is being taken over and/or decaying and/or reused by next wave of humans. But not this time.
Quite fascinating.
[1] what I know is subject to change as time goes by and I get updates
> Around the beginning of the 8th millennium BCE Göbekli Tepe ("Potbelly Hill") lost its importance. The advent of agriculture and animal husbandry brought new realities to human life in the area, and the "Stone-age zoo" (Schmidt's phrase applied particularly to Layer III, Enclosure D) apparently lost whatever significance it had had for the region's older, foraging communities.
I haven't seen any sources citing evidence for Göbekli Tepe post-dating agriculture, but there are many lines of evidence that it pre-dates it -- such as an absence of cultivated grains, granary structures, or other evidence that one sees as agriculture actually gets going. All the plant remains that have been found are wild varieties. Thus the mainstream assumption is that Göbekli Tepe was built by hunter-gatherers.