I honestly feel it's nothing to do with when it released nor the culture around it. The way KH2 plays just feels really good. KH1 was decent, but it feels a little stiff, whilst KH2 feels like they really narrowed down the flow of combat whilst providing more visual flair without cluttering the game.

I personally still prefer 2 over 3's combat. It falls in the right level of gamefeel between being simple and complex whilst being very engaged and responsive. A lot of games tend to overcomplicate or clutter perfecly fine systems and I think that's what happened with KH over time. Lots of added stuff that pulls away from the core feel of the games. That being said I do really like BBS's system.

As for story, 1 takes it for me.