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Seems to contain a rather extensive soundtrack watching the trailer and gameplay videos so far. Would appreciate if someone could take a look at it (is it free to play? seems to require a BaNaPassport) and rip/record it. Thanks.

Ok, that was easier than expected.

Developer is Aiming, composer is Motoi Sakuraba

Account can be created at Banapassport Card site (http://en.banapassport.net/en_US/)
Game runs pretty much automatically at the start with all the obvious hand holding.
Music is loaded as MP3s which can be accessed outside of the flash game as well (I think, please confirm):
Menu music (2:11): http://data.shinra-game.jp/front/sound/20120307_1833/bgm/bgm_01.mp3
Online Lobby music (2:22): http://data.shinra-game.jp/front/sound/20120307_1833/bgm/bgm_02.mp3
Battle music (2:29): http://data.shinra-game.jp/front/sound/20120307_1833/bgm/bgm_03.mp3

I think that's all there is atm music wise.