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Being a master is about being the strongest. Cynthia is the master of Dragon types because she has the strongest Dragon pokemon, Garchomp. That's also why you see trainers like Iris, Lance, Steven, etc profess to be experts or even masters of certain types despite not running mono teams. Steven is the master of Steel types because he has the strongest Steel type pokemon in the world with Metagross, Aggron and so on.
So when Ash says he wants to be the 'Pokemon Master' that could actually be him declaring that he wants to master every single type of pokemon and have the strongest of all types. With that in mind he's the master of:
>Electric
Pikachu
>Dragon
Dragonite (When Cynthia's Garchomp is taken down)
>Fighting
Sirfetch'd
>Steel
Lucario (With Ash surpassing the strongest Steel type in Steven's Metagross and Lucario is shown to be on that similar level)
>Ghost
Gengar
>Water
Dracovish (Only has Cynthia's Milotic and Lance's Gyarados as competition and will surpass both), or Greninja
With that in mind you have to consider what other contenders he has like Snorlax (normal), Infernape (fire), Swellow (flying), Sceptile (grass) and so on.
In that sense the closest to an actual Pokemon Master in the entire franchise would have to be Cynthia or Leon. They both use a wide variety of types with their pokemon being easily among the strongest examples of their typings. Ash surpassing them cements his own steps closer to true mastery.
So with that in mind, Ash is still a long road from being a true Pokemon Master even after this. He doesn't have the strongest Ice, Dark, Psychic, Fairy, Fire, Rock, Ground or Bug pokemon in the world. He has a decent argument for mastery of Grass, Water, Flying, Electric, Dragon, Ghost, Steel, Fighting but he's still a distance from the rest. For example Leon would be the Fire master due to his Charizard being the strongest Fire pokemon trained.
So Ash has more to train and learn to be the master of all.
