I feel the distinction between the schools of thought that go into composing music for games falls into two camps, with the split not really being East vs. West.
One the one hand, you have composers who try to craft music that reflects the mood of the world. This is often compared to film, though I'd argue this is actually much harder to do in games than in movies. Because you might need to alter the song to match how the players actions change the mood of the surroundings, a composer needs to make his or her music modular, something film composers don't need to do. This style of ambient or organic music is most often associated with western game development, notably through masters of the craft like Jeremy Soule and Jesper Kyd. But it can just as easily be seen in the works of Akira Yamaoka or Yoko Shimomura. At the end of the day, this music can be used to associate memories of the places you visited or certain events in the narrative, building a deeper connection similar to film, but in a more personal way as the best scores are often specially crafted to reflect your personal input into them.
On the other hand, you have composers who try to craft music that reflects the actions of the player. This style of composition is most likely what many people think of when they consider music in video games. Older composers had very limited memory to create memorable songs, so many clever composers programmed their music to match the actions of the player to reinforce their limited tracks and attempt to give their looped repetition deeper meaning. The purpose of this style of music isn't really to reinforce the world or bridge a connection to it; rather it represents a bridge between the player and his or her actions as they're represented on screen. Many of the more arcade-focused genres like platformers still retain this style of composition, which you can hear in the works of long time masters of the craft like Manami Matsumae and Michiru Yamane. But there are composers in the "West" who also use this technique as well like Jake Kaufman (aka Virt) and Christophe Heral. Their goal is to reinforce to the player that their actions not only make a difference visually, but audibly as well, and reinforce that through music that's complimentary to the player's actions on the game world itself.
Both styles of music are fine, and personal preferences toward one style or another are often determined by what types of games you like to play. Any distinction drawn that it's an East vs. West dichotomy is just looking at the most surface elements at play. The distinction goes deeper than a mere difference in geography, and instead differs due to the goals about how the developers wanted the player to react to the game's world and the music that brings it to life.
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