Yes you need dollars to play you could exchange Euro's for dollars but not a good idea. You could take dollar travellers cheques which you can obtain in several places tomorrow i.e Thomas Cook safer than carrying a lot a dollars in cash but of course you could break the bank, so good luck.
I should have said but you don't say which cruise line, but some allow you to charge to your cabin account there maybe some restrictions though and certainly you might get carried away so I would be extremely cautious of this option should the line you are with permit it.
They said that they are sailing on the Norwegian Jade(NCL), so they can either use dollers at the tables to obtain their chips or just use doller travellers cheques or a credit card to obtain their chips before play from the casinos own cash office. There are also ATMs available. In line with most activities onboard cruise ships, and NCL ones on particular, expect to be charged for any money changing service you make use of! Happy cruising.