Let us first get the basics down by looking at a simpler phrase. How do you usually say something like "the border between France and Germany"? Native speakers say:
「フランスとドイツとの国境」 formally. ← Needs two と's!
Thus, the formula here is:
"A + と + B + との + Noun"
We do use that second 「と」 when speaking/writing more formally, and I know from experience that quite a few Japanese-learners are not aware of this. Since you seem to be reading the news, you would naturally encounter more formal phrases and expressions.
Now, the actual phrase in question.
From the context, this means "between (South Korea, Hong Kong and other countries) and Japan". Agreed? This piece of news is about how many tourists Japan receives from other countries.
In other words, this part of the sentence is not talking about what happens between South Korea and Hong Kong.
Remember the double-と rule for formal speech?
means none other than:
Or, for more visual appeal, it is saying:
「(Some countries) + と + 日本 + と + の + 間」
Hope you enjoyed my "two - と - rial"!