I don't think the game is intended to be scary - everything that scares you in Minecraft is a result of its darkness and isolation. You are alone, and however much you light up passages and lock yourself up at night, nobody will ever be there to watch your back... and enemies can get absolutely anywhere if you're careless enough.
The atmosphere varies. Sometimes, if it's underground, claustrophobic and dark, and you're running out of torches and hear some really, really creepy sounds, then yes, it has the potential to be scary. But mostly, the actual scares come from surprise attacks from skeletons or creepers. And once you get used to the noises, they cease to be creepy.
Basically, the game can be scary, but it's not the main theme.