Language is flexible, and one (among many) flexibilities is to create meaning by hinting at something instead of outright saying it. This is called "figurative" meaning.
Actually, a "film" is called a "film", because historically it consisted of rolls of long celluloid strips with some pigment on it. Shine light through and the picture is projected onto a wall. Move the strip fast enough and the illusion of movement occurs. This is not how these things work nowadays (we have digital means of storing information), but we still call it "film".
Figurative speaking makes for simpler expressions because often the essence of what you want to convey can be transported in much more concise way:
I go to Rome.
This does not necessarily mean i "go" the whole way: some part I drive, some part I fly, some part I indeed go and so on. Still, you get what i intended to say, yes?
For the same reason you can (and should!) say
I saw a film
I saw the decoding of a digitally stored MP-4 file
you can say
I went to a movie
I went to a specialised place where MP-4-files are decoded for a large audience.
The latter one would be technically correct and still outright ridiculous.