They're a destiny of destiny in their eyes, with Lundqvist chasing his first Cup and the whole St Louis mother thing. They really believe that. Additionally, they've heard it for the past two rounds about how much better their opponents were, ignoring the reality that the Penguins have been in need of a major shakeup for years and the Canadiens were essentially a Cinderella team and without Price.
It's also a part of NY sports culture, which has become a characterization of itself. Any NY team that has a shot at a championship is "the one." This is nothing unique to the Rangers nor the 21st century.
They don't want to listen to the facts, which are as follows:
-the Rangers hold no distinct advantage in any head to head matchup; their primary areas of strength (goaltending and top four D) even at their best are debatably a wash with our own goaltending and top four D
-the Kings beat exponentially better opponents in the first three rounds
-the Kings have worlds more experience playing at this level
-the centre matchup is outlandishly in favor of the Kings
If the Rangers are going to win this series, Lundqvist will have to outright steal at least two, perhaps three games. The forward corps is just too lopsided in the Kings favor, with D and goaltending being too close to give the Rangers any real, consistent advantage.