All of these elements build suspense, the glue that holds a horror story together and keeps the reader interested. Suspense does require one element to work: mystery. Without a mystery pushing the story forward, the suspense has no purpose or punch. In Saw, the mystery is why the two gentlemen were put in the room. In Scream, we want to know who the killer is. Sometimes the audience knows the mystery that the characters don't, like where Marion Crane has disappeared to in Psycho, and the suspense is in waiting for the characters to figure the mystery out. Sometimes the mystery is as simple as wondering who will survive.
A good horror story requires all these elements in order to be effective at purifying built up emotions of fear. A good horror story doesn't even necessarily have to be scary to be effective, as not every member of the audience fears the exact same monster. I may be terrified of, say, clowns while clowns don't affect my friend in the least. In watching a clown horror film, I may be petrified and he relaxed, but the story will still engage both of us in the purging of fear. Even cross-genre piece like comedic horror or sci-fi horror help engage our emotions in fear response should the text employ all of the aforementioned elements.