flying Dubai to Boston USA via Shenzhen and Beijing

Hi, Im a little confused. The requirements for 144hour free transit states non stop flights into mainland china but an example used is: UK – Guangzhou – Shanghai - Hong Kong (two china stops)
Because my flight has a stopover (2hrs) in Shenzhen before my arrival in Beijing, can I use any of the 24, 72 or 144hr free transit to explore Beijing or will i need a tourist L?

On the way to the US, I will have an overnight in Beijing. On the way back from the US I would like to spend 4 nights in Beijing.