Eligibility for 144 hour visa

Of course, you can. Itinerary:

Hong Kong - Beijing - Macau

Is definitely eligible for 144 hour visa free transit in wider Beijing area. It is just important that you do not have any additional landing within mainland China beside Beijing. In Beijing area you can use different airports for your arrival/departure, for example you can land at Daxing and depart from Capital airport or Tianjin airport if you wish.