I don't understand the "true sequel" stuff...I mean, if you were disappointed, that's fine, I can even understand that to some degree, but to write it off as an actual sequel? That's ridiculous. It continues the story and even goes so far as to include major characters from the first. I don't think it's justifiable not to call it a sequel just because they aren't the main characters of this story.
Maybe. Allow me to offer an analogy (because I love analogies).
Orson Scott Card wrote a fairly famous Science Fiction book called
Ender's Game. He eventually turned that into a quartet. Then he eventually went back and wrote a new book based on the events in Ender's Game, but focused on a different character (called Bean). Thus we have
Ender's Shadow. He took that book and made it into its own series.
So, if you followed that convoluted history, now we have a book called
Shadow of the Hegemon. It is the sequel to
Ender's Shadow, but by your criteria it is also a sequel to
Ender's Game. "It continues the story and even goes to far as to include major characters from the first." On one hand it continues the story, but on another hand it is part of a totally different series. It is sort of like those tricksy Photons; it is a particle and a wave at the same time! (or in this case, a sequel and not at the same time). The waveform of sequality only collapses when we observe it.
That seems to be what Kato did; Chrono Cross is a sequel to Chrono Trigger in one sense, but it is also a parallel story that can-but-doesn't fit into a single "series."
To offer another comparison; The Two Towers involves some of the same characters from The Hobbit, it expands the story, etc, but it isn't really a sequel in the classic sense of the word.
It's the same thing as the Star Wars movies. The first three may have sucked, but IV-VI are still sequels to I-III even though the main characters change.
I-III are prequels to IV-VI, but it seems very odd to say that the sequel to Revenge of the Jedi was created a few decades earlier.
But I would like to point out, Star Wars has always been a story of two droids. That stayed the same throughout all six movies (I can't remember enough about the Ewok Adventure and the other movies to comment on those).
I assure you, I meant it by definition only.
Perhaps "Classic Sequel" might be a better term then?