The word sit can work both as a "stative verb" and as a "dynamic verb", so the usage in your quotation is correct.
Note one other word:
I stood in front of the living room, watching the movie unfold at the tv screen while my mom and sister - whose idea it was to watch the film in the first place - sat behind me, on the couch, gasping and chuckling.
This while indicates that during the time you stood in front of the living room, your mom and sister sat (or were sitting).
Neither with sat nor with were sitting would the sentence indicate that their sitting ended with the end of the film. The sentence merely indicates the simultaneous nature of your standing (and paying attention to the screen) and their sitting.
For all we know, they might have been sitting on that couch all day: prior to the start of the film, during the film, and after the film has ended.
P.S. Having read lurker's comment,
You stood watching while they sat gasping. Seems fine.
it might be that Past Tense + ing reads more nicely than the repetitive ing + ing (I was standing watching).