Perhaps, and this is only speculation, the present continuous tense be+see+ing is generally avoided in affirmations such as
I'm seeing Alien 4 tonight
He's seeing a film at this moment.
The verb see also means to meet someone, and said aloud without any previous context, it might be understood that there's an appointment to meet up with someone called Alien, or they are dating someone called Film. I know it's unlikely, as we are all equipped with common sense and personal experiences, but the first two structures do sound a little odd nevertheless, whereas I don't find any ambiguity in the following example:
We were seeing a movie when suddenly there was a loud noise.
The structure be + Verb + ing expresses volition, and there is no significant difference, in terms of volition, between “I'm seeing a play” and “I'm watching a play”, the latter being only preferable if referring to a television broadcast.
Having said that, the present participle seeing + a movie often follows a preposition, and the main verb like. In the Ngram chart below, the clear frontrunner is after seeing a movie with of seeing a movie and like seeing a movie not far behind.
The results shown with the verbs are and were seem to confirm that native speakers tend to avoid the progressive tense with see a movie. This ambiguity, which I mentioned earlier, is easier to eliminate in print and with context, but maybe this infrequency of usage compared to watching a movie, is down to idiomaticity and little else.
(Watching a movie is represented in blue, while seeing a movie is in red.)
If we compare the following results with to see a movie, Ngram produces the following chart.