But Astro, we can go deeper.
If we stand to what you said, it would mean that the reality of the games is the same one of the short series Pokémon Mega Evolution and, for association, Pokémon Origin because in both Mega Evolutions are present.
Let's pretend this is a fact.
So we are at a point in which the Mewtwo from the first movie and the Mewtwo in the game are the same Mewtwo, correct?
But this is a paradox Astro.
And a paradox that would cause us to speak of different universes.
Let me explain: if we take as canon what you provided, it would mean that the sentient mewtwo from the movie and the untamed, beastly one from the Origin one are indeed the same pokémon.
This is obviously not the case, even if they do share the same backstory.
Although we could argue that, as evidenced by MatPat's video, they came from different universes, this would also not make sense.
This is due to the fact that a mewtwo already exists in the universe where the great war that happened 3000 year in the past, the one that made mega evolution a possibility, took place.
That mewtwo is the mewtwo we find in the 2013's pokémon movie, Genesect Legend Awakened, and it has a peculiarity which was left behind, but it's there to be picked up for those who know the story.
Remeber how Doc Fuji's daughter died and pushed him in getting involved in the creation of mewtwo?
You could argue that, as hinted in the movie, Fuji was trying to clone mew and different pokémons for the possibility to bring back at least a clone of his daughter.
In the universe where the Genesect movie takes place, which is the same universe where Mega evolutions, your point of Steven and the other trainer, and some games from the franchise happened, Doc Fuji managed to, somehow, revive his daughter thru Mewtwo, or more precisely AS Mewtwo, as implied by its gentler personality, its intelligence and most importantly,
its female voice.
Coincidence? I think not.
So where does this leave us?
I thought about this and came up with this explanation:
Take two different universes. One where the war happened and thus Mega Evolution is a possibility (A) and one where it didn't, so no Mega Evolution (B).
In Universe B, the one where the games don't allow Mega Evolution, Doctor Fuji's daughter wasn't brought back to life, and thus the created mewtwo didn't have a intellect and became the one we find in the older generations, a beast that roams the cave of Cerulean City. This is the universe where Giovanni would try to appropiate of Mewtwo's raw, untapped power by force so to help himself and his organization in the plan to overtake Kanto.
In Universe A, the one where Mega Evolution is a reality, Doctor Fuji's daughter was brought back to life, so the resulting Mewtwo was just a body, a shell that contained the girl's anima.
This is why in the movie Mewtwo can think rationaly and was able to initiate a partnership with Giovanni, whom this time uses a more pacific approach, and is constantly questioning itself about who or what it/she was.
This would also explain how we can find a Mewtwo in Y/X and the Genesect movie that can Mega Evolve, while in the older generations we find one that can't:
thanks to the Ultimate Weapon created by that man 3000 years ago, that uses the power of dead pokémon to revive, or with a Mega Stone aplify the power of, a pokémon.
This same technology could have helped Doc Fuji revive his daughter, thus creating Mewtwo.