What grammar pattern with 着 does this sentence follow?
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!