Oh yeah, the entity of the face of Mars. Now I'm skeptical but the same thing happened to me. In my case it was because the X files are about the alleged paranormal phenomena that popular culture has long considered as real life facts (although more in the 90's and before that), and I used to be a believer of Fortean phenomena wich is a trully example of modern folklore.
So I guess the Alien for me was always like a fantasy. Despite being science fiction and also despite the possibility of extraterrestrial life, not to mention the sexual nature of the monster. And of course the X Files at the other side of the coin as a show about cryptids, UFOs, chupacabras, Area 51, conspiracy theories, etc. Overall, stuff that mainstream consider (or used to consider) as real.
As for the spooky pareidolia in Big Chap fingers...yeah, there is a ghostly vibe in the shapes and not entirelly a skull vibe.
I think something similar to the uncanny valley takes place, in the sense that you are seeing something that seems human but that you know is not human, which causes you fear.
An interesting video about how vagueness can make things creepy.