Yes, I've been puzzled about this since I noticed the post. I'm inclined to agree that "see" can substitute for "watch" as a sort of idiom when the "watching" is presented in "perfective aspect", i.e., as a act regarded as a point in time rather than as an activity occurring over a period of time ("imperfective aspect"). There is also the flavor of "going out to attend an event" which is more clearly present in "see" than in "watch", as in "We went to the movies. We
saw Silver City", but "We stayed home and
watched a video tape of
Silver City".
I'm going to list some sentences. The purpose for this is unclear, even to me! Maybe they will stimulate further discussion.
I watch movies often.
I'm watching television.
I like to watch movies.
I was watching the movie.
I watched the movie.
I have watched that movie.
I have been watching movies since I was 5 years old.
I'll watch that movie with you.
That's a movie I won't be watching again!
Would you like to watch the play?
Would you like to watch a baseball game?
? I see movies often.
* I'm seeing television.
? I like to see movies.
* I was seeing the movie.
I saw the movie. = I watched the movie.
I have seen that movie. = I have watched that movie.
*I have been seeing movies since I was 5 years old.
*I'll see that movie with you.
That's a movie I won't be seeing again!
Would you like to see the play?
Would you like to see a baseball game?