The German test got my neighboring city (20km) as first choice, and the city closest to my village as 3rd choice. It also featured a city more in the forest area, where I was born - but moved away from after the age of 4. - all part of the Palatine dialect.
So pretty damn cool.
The way the test works is that it uses certain vocabulary like the first and last slice of a piece of bread, which are different in every area, as well as some dialect clues. But the ability of a native speaker should even beat that as you will get pronunciation clues.
I speak high German and have lived outside of my area for 10 years, still a lot of people can identify my origin even if I don't speak the dialect. They have told me that a typical word for my region is "ayo" or "yo" with a kind of rising pronunciation for meaning "That's right". Also for example I pronounce the color "orange" like it would be pronounced in French, due to the proximity of the French boarder, but further north it is pronounced "O-ran-je"(?), actually I forgot the correct way to pronounce it.
I would say the ability to pinpoint other peoples dialect, it depends if I have met a speakers from that particular area before, but especially if it would be a good friend or someone close, and I would meet another person of that particular region, I would be able to tell.
As for other languages as a non native speakers:
I would probably be able to identify the general direction, say north or south, east or west in Dutch, Portuguese and Chinese.
Japanese is difficult, as people learn to speak the standard everywhere now, and I didn't meet many speakers from more dialect heavy places expect the Kansai area (which is easy to identify). But for a native speaker I think it should be easy. The first clue would be the endings じゃ、や or だ、combined with the pitch accent. From the colored maps in
wikipedia one can already gain a very rough estimate, then from there come special vocabulary and onomatopoeia. I think if one would be deeper into the language it should become pretty easy to tell.
I think it is a thing that comes with experience, you meet someone and that person speaks a certain way, and you also get the information where they are from. The more native speakers you meet the more the dots connect.
For English however I would be lost, since my source of input would be from television rather than people, and we usually talk English with other non native speakers, right? Actually identifying a non-native English speakers accent would be much more simple than that of a native speaker here. My old roommate from east Germany told me that people could identify that he is a German from Saxony when he was in Great Britain, solely by the sound of his English.