So which one is correct? I don't like to watch movie or I don't like to watch movies?
"I don't like to watch movie" is ungrammatical; with a countable noun you need an article for the singular form.
"I don't like to watch this move" would be fine, or even "I don't like to watch a movie" though out of context this sounds a bit odd. Perhaps as a response to "would you like to go out for beer, or stay home and watch a movie" ...?
The linked question about "look" vs "looks" is different because both forms are grammatical ("looks" is uncountable and you have "the" in front in both cases). There you really have to understand the difference in meaning.