To further clarify: The game is very much a slow burn. The Thing may jump out a few times, but only when it thinks it has a chance of getting someone, or when it's been exposed. It's main goal is to try and hide, after all.
Several times throughout the game, More things are added into the mix. I'm imagining if you can find survivors of the event throughout the mix, one or two of them might end up being things. Or perhaps A Hand or Head spider will spawn in a part of the level, and will attempt to grab a NPC while they're alone or something.
I'm also thinking that the Thing will never try to turn within sight of the player, in order to obfuscate who the thing is, in order to prevent some level of save scumming. Either that, or the game is effectively death = Restart, which would be a pain if it's a long one.