Does Hong Kong Count as Another Region?

I feel silly asking this but would like to know if I could take advantage of the 72 visa if I were going to fly to Beijing, stay two days, fly onward to Hong Kong to meet up with others and then fly into Shanghai for a longer visit in PRC - for which I would have my tourist type?

Do I put at risk the tourist type that I have for the rest of me trip? Do I satisfy the wording of: "the third country or region"?

Thank you!