I cannot get passed the tutorial fight because all of the shortcut keys do not work. I can assign then but pressing the key afterwards does nothing.

Seems that people over at Steam have work arounds that involve having Steam. No fix that I can find for the GOG version.

Anyone know anything about this?

I had the same issue with a third-party controller, but just fudged my way through the tutorial. Strangely all of my custom button assignments have been working perfectly in the main game since then, so it's possibly just a bug confined to the tutorial.