In White Night, it is not a shotgun, but light itself, that is your only ally, and light in in this game is in terrifyingly short supply.
White Night is not the only horror game of recent years to use light and darkness as inspiration for its game mechanics. Both Shadows of the Damned (an action-horror game with more emphasis on the action portion of the equation) and Alan Wake (also probably more of an action-horror game, though probably with more emphasis on provoking scares than on pure combat) used light and darkness to drive their combat mechanics.
Since both games concern confronting supernatural horrors, it seems reasonable to associate darkness, and the terror that it presents by making things unknowable and obscure, with evil, and light, with its ability to make knowable and to clarify, as a means to combat evil. In both instances, darkness within the environment signals a lack of safety and security in the world, and darkness is also intrinsic to the nature of the enemies in the game—along with the need to purge that darkness with some form of light before making those enemies vulnerable to mundane weapons. In other words, light needs to make the dark things into something that can be combated with things we know and understand, firearms and ammunition.