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奥林匹克运动的故乡流传着这样的几句话：...
This 着 is confusing to me. I suppose this sentence here follows one of these two patterns:
The first one would make sense to me, after all "奥林匹克运动的故乡" is a place, but there's no 在, nor 里 and I don't know why. The second one would make sense too, but what's the point of using a gerund in this sentence...?
All in all, I don't understand what's the role of 着 here.
奥林匹克运动的故乡[n.] 流传着[v.] 这样的几句话[n.]：...
I would break this sentence in three parts as above.
“流传” is the verb here, it means "spread" or "circulating", here it means "these sentences/story goes that..." or "there's a saying ..."
“着” here means the second meaning you listed. It shows the continuity of the verb.
My translation of this sentence is: "In the hometown of Olympic sports, people say:..." It shows the meaning but not a word-to-word translation.
Here's the explanation in Modern Chinese Dictionary《现代汉语词典》:
着·zhe
1 （助）表示动作的持续：他打～红旗在前面走｜他们正谈～话呢。
I'm a native Chinese, but it's my first time trying to explain modern Chinese to language learners. Let me know if I'm not clear enough. Hope it helps!
