I had this as well. The first game I played in the "Chrono" series was actually "Chrono Cross" and I didn't realize it was a sequel until I saw references of Serge & Co.
Then I got my hands on this and played Trigger. All of the previous references on Cross regarding Trigger became totally explained.
Definitely an oldie but a goodie. I have it for my 3DS and still play it from time to time.
I thought it was cool they added the animated scenes to both games. I guess it was their way to reel in more money for re-introducing those games. It worked cuz I bought them. Lol.
Chrono Cross was supposed to be a sequel, but it did so badly that Square said that is was no longer canon. It's a decent game however, it's just a raging Poopasaurus Rex in comparison to Trigger.