These pillars were carved from flint at a time when metal tools were not yet used, demonstrating architectural skills.
More like dogged persistance...
To put it into perspective, by the time the site was built, humans and/or (for sticklers) human ancestors had been using stone tools for more that two and a half million years.
The key word is flint, which is a very fine amorphous or cryptocrystalline hard material which like naturally-occurring obsidian or man-made glass exhibits conchoidal fracture that can produce large flakes when properly struck to initiate a crack that carries through to the edge.
Think of what the breakage looks like when the pellet from a BB gun strikes your window. The pellet strikes the glass, initiating a crack front that propagates in every direction until it meets and goes through the surface on the other side. The cracks which go laterally almost 90 degrees from the BB trajectory can go a long way with a circular fron to make really big flakes.
This process is how sharp tools, like arrowheads, were made in the stone age, and sill are. Here is an example how this process, called "knapping" is done:
You can't do this very well with crystalline rocks, igneous (granite), metamorphic (marble), or sedimentary (sandstone, limestone, shale) because the cracks don't propagate th same way.
It's my guess that the stones of Gobekli lent themselves to the knappin procee of carefully striking out pieces with directional blows that removed fragments just wher one wants. Note that te artisan in the video used a piece of elk antler to gt some big flakes. But I know that Our North American natives used the deer antler points to make the smaller chips as well. (actually, in the Houghton, Michigan mines, the rocks there have large copper nodules that could be pounded into knapping tools, but not very good knives.)
Or maybe my imagination is just working too hard for this perceived possibility of how Gobekli's animals and plants were inscribed on flint rocks without carbon steel chisels and hammers.