The checkout wizard will usually create javascript code that will change the state select list into a state text field and make it not required. If you removed that code too, maybe the best thing to do would be to run the checkout wizard again to re-generate it. It doesn't appear that you have done much other customization to the checkout page itself, so a fresh start might be the best option since that code would be complex to add back by hand.
Actually I viewed your source code on the checkout page, and maybe you do have too much customization to make re-running the wizard practical.
I could help write the javascript to swap out form elements and make the text field not required in a premier support ticket if you want to go that route.