Sorry, follow by my last question, i've checked
https://bulbapedia.bulbagarden.net/wiki/Marowak_(Pokémon)
 

And based on my understanding,
1. Marowak-Alolan is a gen 7 poke, there's no gen 6 TM set to follow, so "it cannot learn TM-Dig on gen 6" is not true

2. When it first released on gen 7, it can learn TM-Dig, there's no any gen a Marowak-Alolan cannot learn the TM-DIg

3. I let it learn TM-False Swipe in game (not from move relearner) and success, so what makes the different? Why "it CAN learn TM-False Swipe on gen 6"

 

You've proved the Marowak-Alolan cannot learn TM on gen 6 by
https://bulbapedia.bulbagarden.net/wiki/Dig_(move)
so please check also the
https://bulbapedia.bulbagarden.net/wiki/False_Swipe_(move)

it does the same thing.
 

Just want to know the game mechanism in PRO, because I bought the poke, and found out it cannot use the move, which i think doesn't make any sense to me, thanks for your time.

Edited October 17, 20205 yr by Dreamvil
add prove

Never mind, I think you are correct. We should follow the move set on Sun/Moon, but TM-Dig only exists in Let's Go Pikachu/Let's Go Eevee version, both are gen 7 but not having the same move set. The info display on pokemondb.net is more clear. Can help to closed the topic, thanks.

Edited October 17, 20205 yr by Dreamvil