Yes, you should respond to the letter with a copy of your original return for 2015, and the W2G showing the winnings were for 2015, and recorded on your 2015 tax return. Send an explanation (similar to the information you provided here) with your forms. Be sure to keep a copy of everything you send.
If they have a different form and/or amount for 2016, they will advise you and you can go forward from there to pursue resolution if there is still a question.
Any Forms W2G from the casino for 2015, would be sent to the IRS in 2016.
