I'll arrive to Hong Kong by flight Etihad Airways, then I'll have to move to Hung Hom station.

No, you cannot. It doesn't relate to the airlines.
The free shuttle bus service means that you can take free bus to the hotels after arriving at AE Stations (HK, Tsing Yi and Kowloon Station) as long as you purchase the AE ticket.

Thus upon landing, it's suggested to take bus no.A21 at Airport (Ground Transportation Centre), and get to Hung Hom Station directly. The whole way takes around 75 mins. It costs 33 HKD per person.