Did the premise of an entity approaching you only when it's not being viewed originate with Doctor Who's Weeping Angels?
The Weeping Angels apparently originated with Steven Moffat seeing a statue of a weeping angel in a structure in a cemetery and returning later to find out it was gone. At least according to this RadioTimes article. They first appeared in 2007 in the episode Blink.
I am wondering if this mechanic has been done before though?
It's become quite common in the indie horror scene.
In the 2007 video game Sherlock Holmes: Nemesis Watson would not move if in the player's view but would teleport behind the protagonist when given the opportunity. A video of it can be found here.
Considering this could be an easy place holder for developers or a way to get around programming walking animations all together I'm surprised no one took the idea and ran with it before then.
All that said it could have been used in books or movies. Maybe a twist on some other vision-centric myth like Medusa or Orpheus and Eurydice?
Funny enough, a number of years ago a giant 4chan archive surfaced which included a lot of the very first SCP posts that had been lost. It actually confirmed that 173 was posted after Blink aired, meaning it was almost certainly inspired by the episode. Not that it makes the SCP worse, but it's some interesting lore.
There was a segment in the 2005 game "Condemned: Criminal Origins" where mannequins in a department store at night would only move (and surround you) when you weren't looking. Scared the shit of me way back then.
Check out They Bite by Anthony Boucher, written in 1943.
Edit: this is my favorite horror short story. Read it at night if you want to start jumping at every shadow in the corner of your eye for the next three days or something.
“Observation” in quantum mechanics doesn’t mean a person looking at them, it means taking a measurement, which involves interacting with the particles somehow. It’s that interaction that causes the particles to behave differently. In other words, photons behave as a wave (moving according to a wave function) until another particle interacts with them, at which point they behave as a particle (moving in a straight line). See the various different double slit experiments for evidence of this.