Do you mean story-wise? If so, there are, of course, some references to KH1 and CoM here and there, and some unexplained scenes that no first time player would understand even if they played the prior games, but as far as the main point of the game is concerned (beat the main villain and maybe get to know his motivations), then I'd say you'll be fine. Be aware that it's been years since I played that game, so maybe I'm wrong about some stuff.
If you mean gameplay-wise, the system is simple enough to understand, once you unlock an ability, all you have to do is read its description and equip it, the rest is up to you. Drives and Summons are also very simple to use.
Oh, by the way Roy, I want to let you know of something about each version of KH2 (except the vanilla one).
-The PS2 version is the 2nd best one, but I'd say it's the best version if you don't mind 30 FPS and load times, since every mechanic works. People have said that a certain gimmick enemy can now be beatable under base Lv 1 conditions (read: no stat boosts are required). You have to beat it under a certain amount of time to 100% complete the game, which was deemed impossible to do until the PS4 version came around. Some time later, people found that it was indeed possible to do on the PS2 version.
-The PS3 version is the worst one overall, since it doesn't have any improvements over the PS2 version besides graphics and the possibility to play the game with English subs without patching the game, and it has worse load times than the PS2 version. Avoid at all costs if possible.
-The PS4 version can be considered the best version by a lot of people, since this version has pretty much no load times, has superior graphics, and runs at 60 FPS (which made beating that gimmick enemy possible). However, this version broke a mechanic, namely, Blizzard. The finisher variant of that spell let you deal extra chunks of damage while ignoring a value that lets bosses to break out from your combo. This is no longer possible to do on this version, which is why I consider the PS2 version to be the best one (again, if you don't mind load times and 30 FPS). Every other mechanic works as intended though, only Blizzard suffers in this version.
Just something to keep in mind.
As for DMC2, you're probably the second person I've seen to have something positive to say about that game, but you went a bit more in-depth with said positives.