does it have to be non stop?

If you are a Chinese citizen, then you will be required by Chinese authorities to travel on your Chinese passport. In reality and you know that even better than myself, that while in China you are considered to be a Chinese citizen first. OK, let's assume that you will use a US passport and in that case your itinerary is not eligible for any kind of visa free transit because your immediate points before and after Shanghai are in Hong Kong. Simply speaking, the basic rule of 144 hour visa free transit requires that immediate points before and after a Chinese destination have to be in two different countries or eligible territories (eligible territories: Hong Kong, Taiwan and Macau).

In other words, your itinerary would be considered by Chinese authorities as a round trip or return journey because your immediate points are both in Hong Kong. So, you will have to adapt your itinerary to looks like (for example):

Los Angeles - Shanghai - Hong Kong

The above is an example of eligible itinerary for 144 hour visa free transit. So, the answer is, yes, it has to be a nonstop flight.