Oh yes, that's right, Tasjo! Some sites do directly load .MP3 (or other formats) audio files into their webpage's general-purpose SWF player, rather than embedding each selection into it's own dedicated player.

This make things more easy! Just play the soundboard and save-out all those .MP3 files thereafter sitting in your browser cache ... and you're done. Most browsers have easy access to their cache or, as Tasjo suggests, there are browser plug-ins to do any heavy-lifting for you.

Life is easy in the year 2015 A.D.!