Hainan to Beijing

Unfortunately, they are not eligible for 144 hour visa free transit scheme. Simply speaking, you cannot have two mainland Chinese destinations in a row within your itinerary. Also, the countries immediately before and after your mainland Chinese destination have to be different. Beside the countries, it is allowed to use Chinese territories of Hong Kong, Taiwan and Macau who act as third countries in this regard. An example of eligible itinerary is:

Singapore - Beijing - Hong Kong - Singapore
Singapore - Beijing - Kuala Lumpur - Singapore

In reality, it is quite simple...