I am not a copyright lawyer but I play one in Phoenix Wright.
become those musics time-barred somewhen?
I'm having trouble trying to figure out what you mean, but yeah, it will eventually become public domain. 75 years or so in da US, probably the same or less in Japan.
does it depends, how the music was registered back the?
Nah, international copyright law has been pretty static since video games have been around
does it depends, if it's about old chip tune music or red book audio?
No. What does depend is if a musician licensed their work to the game company, but kept the rights to it.
does the copy right belong to the composer or the company which has/had the game rights?
Depends on the circumstances. 99% of the time, especially with older games, I'd say it belongs to the same guys who own the game.
and if the company doesn't exist anymore, what happens then?
Whoever bought the company owns the rights. If no one bought the company, then it might either revert to the original creators or be considered public domain depending on the country.