SonicWaffle said:
So, forgive my ignorance, what's the problem? How can Rockstar sure someone for using a name which was in use even before they made the game?
Trademarks only cover specific things. So, for example, a while back a lot of people tried to mock Cadbury's for trademarking the colour purple, without understanding that the trademark only covered chocolate bars and similar items. Obviously it's reasonable for Cadbury's to want to prevent people from making products that look the same and might fool people into buying the wrong thing.
In this case, Rockstar's trademark probably covers an area along the lines of "multimedia", while books would fall into a different area. So no-one can make a computer game, TV show, film or anything similar named LA Noire, but a book probably wouldn't enter into things at all. That means Rockstar aren't infringing anything since even if the book is trademarked, it's a different area, while the TV show could be infringing on Rockstar's trademark. However, it's worth noting that this hasn't actually gone to court, so no-one's determined that anything actually is infringing anything else. It's just close enough that Rockstar are probably legally obliged to defend it just in case, as others have already noted.
It's also worth noting that different countries treat trademarks differently. In some, trademark protection depends to some extent on market share. So it's possible that the book simply isn't that popular, but there are concerns that the international trademark status might have problems if the film is popular.