I think this is kind of an interesting question, so I'll give it a shot. Despite the "or," your example is not an alternate title but rather a [subtitle](http://en.wikipedia.org/wiki/Subtitle_(titling)) (not to be confused with the subtitles on a foreign-language film). In modern times, subtitles are more commonly set off with colons, as in the subtitles of Avatar: The Last Airbender or Ryse: Son of Rome (not films, but you get the point). Frequently subtitles are used to distinguish members of a series, as in Transformers: Dark of the Moon or The Hunger Games: Catching Fire (a convention that didn't start, as far as I can tell, until the 20th century).

So why the "or"? Film titling traditions come directly from book titling traditions, and these are what Kubrick was alluding to. In modern books, subtitles mostly appear in nonfiction titles to explain an unclear title, e.g. Freakonomics: A Rogue Economist Explores the Hidden Side of Everything, or The Audacity of Hope: Thoughts on Reclaiming the American Dream. In the nineteenth century and earlier, subtitles appeared quite often in the titles of plays and novels as well, and by at least Shakespeare's day (at least in English), it was a common but by no means universal convention to set off a subtitle using "or." Examples include Shakespeare's Twelfth Night, or What You Will (~1602); Aphra Behn's The Rover, or The Banish'd Cavaliers (1677); Samuel Richardson's Clarissa, or, the History of a Young Lady (1748); Mary Shelley's Frankenstein, or The Modern Prometheus (1818), and so on. The two most famous twentieth-century examples I can think of are J.R.R. Tolkien's The Hobbit, or There and Back Again and Kurt Vonnegut's Slaughterhouse-Five, or The Children's Crusade: A Duty-Dance with Death (which has a double subtitle).

This last paragraph is mostly speculation, because I'm not sure when the "or" originated or when exactly it went out of fashion. I don't think it ever served the purpose of denoting an alternate title, though. By the late 19th century the "or" seems to have fallen out of fashion, and all subsequent uses of it seem to me to be somehow atavistic: either parodic, as in every work by Gilbert & Sullivan (The Pirates of Penzance, or The Slave of Duty, etc.) and in Kubrick's and Vonnegut's subtitles, or a sort of nostalgic throwback to an earlier period of literature, as in Tolkien's subtitle. Kubrick and Vonnegut are both famously allusive artists, and I think the sense of alluding to an earlier time helps them to set their brand of despairing comedy in historical context—but now we're getting a bit too literary-analysis for this subreddit. Anyway, I hope this was helpful. (edit: grammar)