Depending on how exactly a particular game uses the DSP, you might be able to patch Dolphin (specifically DSPHLE) to dump decoded audio before it gets mixed with other effects/music (basically, audio dumping with multiple tracks). And you can use Dolphin to extract files from the game ISO. All the steps in between are handled by code in the game itself, so there is no general solution.
Another way to think about it: your question is almost equivalent to "how do I extract all the sound effects from a Steam game using Windows".
Another way to think about it: your question is almost equivalent to "how do I extract all the sound effects from a Steam game using Windows".