There was another version completely different, though it did deal with asphyxiation.
A little boy in a mental institute for children kept drawing the monster on a piece of paper when they were doing "art" I guess. So the nurse asked what the monster was. The kid said it didn't have a name, but if he took his eyes off it, it would kill him. It only "appeared" at night, and the kid was known for losing a lot of sleep and was on medication for it. The nurses thought nothing, that he was probably dreaming. That night, the kid dies, courtesy of asphyxiation.
The room was watched for three days, with no sign of any "monster". Workers were interviewed for murder, but none of them showed up clean. The case went unsolved.
I don't know where you people got the military story from, I've never heard that version. It's interesting how it supposedly moves that fast, and is at a military base for some reason. Right.