I don't see why movies should be any less "classic" than books. A Tale of Two Cities was published in 1859 and is still a classic - why not Casablanca many years after its creation?
Movies, on the other hand, can date because of technological changes (silent vs spoken vs color etc), ways of acting (we don't expect modern actors to act in the theatrical way of those in early cinema), different editing techniques (a 70s series like Kojak looks unbearably slow compared to a modern police series), and even what they were allowed to say (movies being more heavily censored than books can look way more quaint the older you go).
An overuse of special effects and fast editing since the 80s has also done much to alter the tolerance of modern audiences for subtler movies.