James Cameron's movie actually borrowed a LOT from "A Night to Remember" (the movie)
As far as video games, there's been a project going on for the past 10+ years called Titanic: Honor and Glory which looks amazing, they're trying to replicate everything as perfectly as possible. The original creator seemed to get distracted too easily and left the project several years in, so that's why it is taking so long to come out, but it is still a very cool project and they have some downloads that have a majority of the ship you can "walk" around.
Regarding the "romantic" aspect (not as love but the idea of the time period) I think part of it was a fascination of the time period and the ending of the Victorian era, different classes of passengers, the stories from survivors, the fact that the ship was somewhat afloat for well over an hour allowing a lot of events to take place, etc. made the story more interesting than one that would have sank immediately. Also the theories about the previous damage playing a role, maiden voyage, etc.
It was absolutely a tragedy but we feel far removed from it being over a century since it took place.