There are many movies made about the winning team, and rightly so. Supporters often make sycophantic documentaries, opponents often make vicious fantasies, but in either case they're about the winning side, not the losers.
So "Game Change" is an oddity. It's worth pointing out that, while this is an HBO film, it was made with an all-star cast: Julianne Moore, Ed Harris, Woody Harrelson. Why was it made? Possibly the film-makers thought Sarah Palin would be in the midst of a Presidential run at this point and this movie would be relevant (and *cough* hurtful). Possibly they really thought the story was interesting and worth telling - although the events portrayed happened just three years ago and there are no new revelations in the film (from what I hear).
What I think motivated the filmmakers was simply schadenfreude. The election of 2008 was so cathartic that they needed to relive it in just one more way. Well, good for them.