I'm not sure if anybody has noticed this yet, but I figured I would post it here anyway.

The 1986 film version of Hokuto no Ken features songs that weren't included in the official movie soundtrack. I don't know why it was like this, and I find it very confusing.

Is it possible to somehow rip the music from the film itself or what?

you can rip it yourself, with sfx and all if you want.

The thing is, if it WERE possible, I wanted to know HOW I could rip it :P

try this
https://mega.co.nz/#!mFBGVR5J!LQlc-x4nd4HpHVfsPE-9DS3BQzz1VV3ZTU8oF9QsXts

after yo install it, you run the software, it will appear a welcome window with stuff to do, you chose the recording part.
Make sure you are selecting Device and Line in with your proper audio of your computer.

see this pic -> https://mega.co.nz/#!vBhwQaqZ!qg5chEMo8oHw0BGaa620hCCO3SdtY1jJpdpPALv geoI

Is this what everybody else uses to rip unused soundtrack songs from movies/films/TV shows?

no. but that depends on the choices of some people.
I use that.