I currently have an arcade stick I made a while ago, which I want to use in a project with my Pi, which will run a simple scratch project. The Arcade Stick connects to the Pi through USB, and I can't find any way to bind the Arcade Buttons to keyboard inputs.
I'm not 100% sure how you'd detect inputs from the joystick, but you can probably use a python library like Pygame or PiBorg. You could then read this to see a few ways you can emulate a keystroke. In the end, you would have a simple python script that's running in the background, which would convert your joystick movements to keystrokes. If you'd like you could create a service and have the python script automatically run at bootup with systemd.