A movie is a recording of the past, the blessing is not happening in front of you when watching the movie. It’s documentation of an event that already happened. You do not have to amen the blessing because the blessing was actualized in the past. You are not a witness to the blessing when watching a recording, you are a witness to documentation of a past blessing which is fundamentally a different event. There is a similar question/answer here, noting amen are not required for prerecorded brochos.
From my limited understanding “amen” could mean “let it be” or “so be it” or “may it be so” or essentially “please let it be as we have prayed”.
If the blessing was in the past, to add “let it be” maybe superfluous since that which is to be blessed could have transpired.
Additionally, in the context of a movie, one who says “amen” to a recording is attempting to invoke the power of God (the real God) to help in matters which were scripted by human writers. Should we not invoke God for more significant ends, such as to end the suffering of people?