Disclaimer: I have no idea. However, if the game runs on MAME you may be able to log its music and create a soundtrack in VGM / VGZ format, more pointers in this forum (which requires an account to read it) https://vgmrips.net/forum/viewtopic.php?t=3561 and you may requests someone to rip it at this forum https://vgmrips.net/forum/viewforum.php?f=17 (vgmrips would be the place where you'd publish the set after doing it.)
ah, crap, I keep forgetting to reply to this topic.
Unfortunately, I'm pretty sure you're basically out of luck in terms of getting a full, proper rip of the game. It doesn't seem to have any kind of service mode/menu, let alone a sound test.
You're also unlikely to ever see it supported by a logging format like VGM, because the music is played via a custom sound chip that was only used by a handful of SNK games in the early 1980s. There just isn't enough interest for someone to put in the hard work adapting the VGM format to emulate this extremely old, poorly documented hardware.
On the other hand, if you're comfortable with MAME, you can use the slider controls menu (accessed from the main menu, which is called up by Tab with default keybindings) and turn down the volume on the sound channels that play the sound effects, "Samples" and "Discrete Sound". Then only the music will be heard.
If you open MAME with a command line prompt, you can add -wavwrite fantasy.wav as an option to log all audio that plays to an uncompressed WAV file. Or F12+Left Shift+Left Alt will record what you see/hear to an AVI file.