To clarify since it isn't clear from the original post, Gobekli Tepe is not itself a city but rather a temple complex that was likely used by semi-sedentary or fully mobile hunter-gatherer groups on a seasonal basis.

Since this is not a city it doesn't really change the timeline for the origin of cities and urbanism, but it does alter what sorts of traits we talk about as being essential to urban-life. More of less prior to Gobekli Tepe it was believed that mobile hunter-gatherer groups didn't construct monumental architecture (like the temple-complex at Gobekli Tepe) due to a lack of a large pool of labor and the central leadership necessary to organize that labor. Gobekli Tepe demonstrates that this isn't the case, that hunter-gatherer groups could build these sorts of monumental architecture. Gobekli Tepe isn't the only evidence of this, as Poverty Point in Louisiana and to a degree the Norte Chico pyramids of the northern Peruvian coast are examples of monumental architecture constructed by hunter-gatherers and sedentary semi-agricultural people (for Louisiana and Peru respectively).

In short, what Gobekli Tepe changed in our view of the past was the idea that monumental architecture was developed after sedentary agricultural life. Gobekli Tepe (and these other sites I mentioned, among others) demonstrates that monumental architecture was feasible for hunter-gatherer groups and actually precedes sedentary agriculture.

Edit: To answer your second question, it is widely accepted by archaeologists that sedentary agricultural life isn't a prerequisite to construct monumental architecture. This isn't very contentious anymore.