Apparently someone is making a game about the Titanic. Their goal is to have the entire ship explorable and there will also be a story mode, though no details have been released yet. As some who has always been fascinated with the Titanic, I will definitely be keeping an eye on this project.
http://titanic-honor-and-glory.tumblr.com/The only other game about the Titanic that I know of is Titanic: Adventure Out of Time, a point and click adventure game from the 90s. It was a fun game with an interesting story and most of the ship was explorable. I hope this one will be similar.