While I can't say I'm an expert in the era's of video game music, I can give a theory that I have come up with to describe what I feel has had the most influence on it.
A calculus teacher of mine once described "the holy trinity of classical music:" Beethoven, Mozart, and Bach. Beethoven was seen as a composer who could wrap his mind around an idea and create a symphony. Mozart was able to instantly create music that was easily remembered, a true genius. Bach was a man who really put the emotion into the music.
I then applied that to whom I consider the "holy trinity of video game music:" Uematsu, Kondo, and Mitsuda.
Kondo has the gift of taking melodies and getting them recognised by a large amount of people. Look at Super Mario Bros. for example. I have seen parties stop just because somebody starts playing the SMB Overworld theme on a nearby piano. The parties then turn into a request for more. Kondo also did well for Legend of Zelda, which has just as much recognition as Mario.
Uematsu has music that matches the game very well. When playing FF7 for the first time, I actually felt like the theme from Cosmo Canyon actually belonged. Aeris's theme brought me to tears, although seeing her die brought me to tears as well, (because I wasted so much time leveling her up.) And I was thrown for a loop when I heard One Winged Angel, just because of the complexity.
Mitsuda has a talent of putting a story in the music alone. I heard the Chrono Trigger soundtrack, and was litterally blown away at the variety that was put forth. I then managed to fall in love more with the celtic sound of Chrono Cross. The point of his music is that you don't have to understand where the story of the game went to understand a general plot of the music itself.