First off, I'm not certain how fast the warp velocities necessarily are. Yes, they seem to be faster than in the prime universe, but the relatively short trip from Earth to Vulcan still seemed like it took several hours in the first movie.
Anyways, the video game theoretically happens between Countdown to Darkness and Into Darkness - it starts with the Enterprise being diverted by a distress call (versus the normal mission start to Countdown to Darkness), and also ends with a trip to Nibiru. The video game covers 2259.32-2259.33 - if the Mudd comics ended the day beforehand, that would put it 24 days before Into Darkness, close enough to a month in my book.
We don't know how long the Enterprise was at Nibiru, do we?
Of course, other problems call the game's events into question - the Gorn reference in the movie, again the "nobody died" line. But then, the Tribble comics have a stardate about 100 days after the bulk of the movie (and during the refitting period unless I missheard Kirk's speech at the end). I wonder if there were late script changes giving it an earlier date and adding that scene with Pike, or whether this stuff wasn't actually being vetted as strictly as is implied.