I've just copied the the bit that made me interpret it that way, I don't know how to highlight but it says about having a ticket to a third country I was assuming 1st country is where you come from second is Shanghai and third is where you are going before you go home to make Shanghai your stopover?
* I ended up calling the hotline they said you could visit the other country before or after Shanghai. It was just the Third country but that confused me.
A: A citizen from certain countries can transfer in China via any of the following ports of entry including Shanghai Pudong International Airport, Shanghai Hongqiao International Airport, Shanghai Port International Cruise Terminal, Shanghai Wusongkou International Cruise Terminal, Shanghai Railway Station, Nanjing Lukou International Airport, or Hangzhou Xiaoshan International Airport without a Chinese visa by producing his / her own valid international travel document and onward air / vessel / train ticket to a third country (region) with confirmed date and seat within 144 hours upon arrival, and can stay within the administrative precincts of Shanghai Municipality, Jiangsu Province and Zhejiang Province for 144 hours.
13.Q: If I, an Australian citizen, plan to travel from Sydney to Shanghai and then back to Melbourne by air, can I apply for 144-hour visa-exemption transit?
A: The policy requires that a foreign passenger book his / her onward air / vessel / train tickets with confirmed seat in advance and leave China within 144 hours for a third country or region, and therefore it is our suggestion that you change your flight ticket to Melbourne to one bound for a third country or region such as Hong Kong, Singapore or Kuala Lumpur, and return to Melbourne afterwards. Such an arrangement will enable you to meet the requirements for 144-hour visa-exemption transit.