Does Square Enix give out "reusable" codes though? What actually happens when the second person enters the same code to be redeemed?

I would assume they just get a "this code has already been used" error. It's not SE giving out duplicate codes, it's the scammers.

Either that or, as I said earlier, if the third-party site is giving out genuine codes for less than the original purchase price, then they're probably stealing the credit card details of people who buy from them. There's only one supplier of the original codes, and that's Mog Station - so someone has to purchase the code at their fixed price, whether it's you or them.