The case
The 1994 film was an event: Cruise as Lestat, Pitt as Louis, a young Kirsten Dunst. The poster and the title card read "Interview with the Vampire," the same as the novel that had been on shelves since 1976.
Almost everyone says "a vampire." Anne Rice's title is specific, one particular vampire being interviewed, but the generic article is how you'd naturally describe the premise to a friend.
Why our brains do this
Definite articles in titles get swapped for indefinite ones because that's how we describe a story in conversation.
Sources: Wikipedia — Interview with the Vampire (film) · Wikipedia — False memory: the Mandela effect
