The defining thematic element of both Vampire: The Masquerade and Vampire: The Requiem is personal horror.
In roleplaying games, horror is traditionally invasive. Games such as Call of Cthulhu or Chill depend on a fair degree of contrast: the characters are decidedly heroic defenders against incursions from the unknown. Horror comes from recognizing that the universe is hostile, or that evil exists outside of the characters.
In contrast, the Vampire game's focus is on the character's own evil. A Vampire is a character who is fundamentally unable to control himself under specific circumstances, whether due to specific events (such as frenzy) or the constant degradation of the character's humanity as the story progresses. Vampire is therefore not just a horror game, but a tragic horror game - the characters are evil, become progressively more evil, and are aware that these are conscious choices that they have made.