"I like the movies."
Translation:Μου αρέσει το σινεμά.
Μου αρέσει οι ταινίες is still not accepted
No, of course not. The subject οι ταινίες is plural and so the verb has to be αρέσουν.
("the films do not appeal to you", plural, rather than "the films does not appeal to you", singular.)
Μου αρέσουν οι ταινίες would have been accepted.
From κινώ (to move) comes κίνημα (a movement), plural κινήματα (stem κινηματ-); from κίνημα "movement" + γράφω "write" comes κινηματογράφος ("movement-writer" = cinematographer) for the person and κινηματογράφο for the place where moving pictures are shown.
This word became cinématographe in French -- with sound changes as if the word had come into French from Latin -- and Kinematograph in German.
Rather a long word, it got abbreviated to cinéma in French (whence English "cinema") and to Kino in German (I'm guessing the Norwegian word is borrowed from German rather than having been shortened from kinematograf independently).
That English or French word then got reborrowed into Greek as σινεμά.