- What are you doing? I'm WATCHING a movie.
- Have you SEEN that movie already?

If watching a movie is something you do intentionally, why would it change from "watch" to "see"
I believe we use it (see) idiomatically when we say "Let's see a movie this weekend." or
"Have you seen the play, Lez Miserables?".

Finally "to watch" denotes present tense
and have you seen denotes past tense in the way you phrased the question

But in all the cases thanks for the information.