Because the film in this sentence not in dative but in accusative, so it takes "den".
The dative in this sentence is only "the changes" because it comes after "with" - "mit".
Let's say that there are two versions of the film, the original release and a director's cut with some changes, and the speaker likes the one with the changes.
Before reading these comments, I thought the intent was more about the plot. So my suggestion was "I like the movie with the twists." Does that also make sense here or is there another way a native speak would say that?