I would feel fortunate IF I ever won enough to worry about it. Then I wouldn't worry about it.
You pose an interesting question though, I have never seen it posted anywhere on a cruise ship that winnings above $600 have to be collected at a separate cashier or otherwise somehow reported and recorded. Based on this, I would tend to believe you do not have to report gambling winnings above the $600 threshold.
If you realize there may be multitudes of passengers from a dozen different countries on each sailing, trying to keep track of the various home country laws governing their citizens aboard foreign vessels might be just too much to be considered.
I would say WIN,WIN,WIN and if you have to do something legal about it they will let you know.