That analogy does not work because in all the cases you describe a copy of the movie ends up with the viewer.
When you connect to a remote server over a computer and upload data and receive back results produced by the server software you do not receive a copy of the program. You receive a copy of the output that the program produced.
When you connect to a remote server over a computer and upload data and receive back results produced by the server software you do not receive a copy of the program. You receive a copy of the output that the program produced.