I am a huge Star Trek fan and I happen to think that Into Darkness was a fantastic film that did the Star Trek Universe well. It had the right mount of action along with the right amount of story. People who hate on it are too fond of themselves and are not comfortable moving outside of their box.
So to the original question; did the official game hurt the movie? No, I don't think it helped, nor hurt the movie. The game was garbage to begin with. Who in their right mind wants to play Kirk in a third person shooter. Now with that said, I gave it a shot anyway because as I said above, move out of your box and don't be so narrow minded. Even with giving a fair shot, I still think it would have been best if the game had never existed. The movie was phenominal and I even bought the Blu-Ray with all of the fixens with it.
Bottom line, people need to stop hating on new ideas in classic universes. Into Darkness was a great fit and I look forward to another entry into the series.