Nope, the Prinsendam is registered in the Netherlands.
I was on an Alaskan itinerary at the time. The casino Manager informed me that any winnings over $1300 required a W-2G issued by Carnival Cruise Casino. Interesting point though...was it only because we were in Alaskan waters? Or perhaps it is a policy of Carnival (HAL parent company & casino operator).
Hopefully you already itemize your deductions on your taxes. When you itemize, you can deduct gambling losses up to the amount of your winnings. I'm not a tax expert, but if you won a couple thousand, I would deduct the whole amount. I can't see anyone at the IRS not believing that someone would have a couple thousand in losses to offset winnings. If it was more than a few thousand, that gets tricky.
If you take a standard deduction on your taxes, then you wouldn't be itemizing in order to deduct your losses.
My husband won $4,000 on a poker machine last year on Carnival, Destiny. He got a W2-G. We had to claim it on our taxes this year.
2/13/09 Carnival Paradise
2/22/09 Freedom of the Seas
83/Azure Seas; 84/Song of America; 88/Stardancer; 92/Jubilee; 96/Viking Serenade; 97/Holiday; 99/Enchantment OT Seas; 00/Elation; 01,02,02,03/Ecstasy; 02/Voyager OT Seas; 03/Victory; 04/Adventure OT Seas; 05/Sapphire Princess 05,05,05,06,07/Monarch OT Seas; 06,07,08,08/Paradise; 06/Freedom OT Seas; 07 Pride; 07 Pearl; 08/Valor; 08/Serenade OT Seas; 08/Coral Princess