>>36393336Postgame is the meat and potatoes of Pokémon. That's what makes or breaks it. But a second region isn't something that constitutes postgame because it's one-and-done type of content.
What people actually mean when they say "postgame" is the longevity of the game through replayable content with lasting appeal. Battle Frontier is the most common example of this, and some other good ones include the PWT, the Black Tower/White Treehollow, gym leader rematches, and even auxiliary content that's fun and repeatable such as the Pokéathlon and Sinnoh Underground's digging minigame.
If it's a one-and-done type of thing, such as the Delta Episode, Ultra Beast quest, or legendary Pokémon hunting then it doesn't count. That kind of stuff doesn't add real longevity to the game, it's more of an extension to the main story.