A similar announcement was just made for the full game but this is for the FREE DEMO.
I have tested things out, but I imagine there will be some issues. If you are willing to try it out and offer feedback before it goes to the default branch, you will need to enable the "testing" beta.
Go to "Islands of the Caliph > Properties > Betas" and select "testing" from the drop-down menu.
There you will be able to rebind the keys to your controller sticks and buttons.
Note: The game requires the use of the "Enter" key and "Tab" at this time. Also, at this time if you are selecting a number in the inventory dialogue or other places, you will still need to type the number on your keyboard. I will address this in the next couple updates, before it goes to the default.
Also Note: You will need to restart the game to use this update. Trying to load an older save file will show you an error, and direct you to the manual.