Hello Marta,
Thanks for stopping by to ask me a question. While I have never personally been on a Disney Cruise Line cruise, I was able to reach out to
Marcy, one of my fellow panelists who is one of the Disney Cruise Line specialists here on the panel.
According to her, there are board games in the lounges, but technically they are for use in the lounge. However, she suggested that you could ask the cast member if you could take it to your stateroom and then return it as soon as you are done. I can't guarantee that this would be allowed, but it never hurts to ask. She said that the board games are in the Promenade Lounge on the Disney Wonder.
Another suggestion she offered was shuffleboard on Deck 4. She said that while it isn't technically a "board game", her kids love to do this.
If you have any other cruise questions, feel free to reach out and ask Marcy or the other two Disney Cruise Line specialists, Diane W and Dolly M. They'd be happy to help you out.
Have a wonderful time!
~Allison L