Currently it's possible that Socks is protecting Story's identity and remembers him just fine. Alternately, Socks had a personal epiphany and Ashe is just showing us his internal train of thought in a far more fascinating way. Although I am not responsible for anything that happens to anyone who chooses to disregard Story's existance.
Labyrinth never states that the child needs to be a human, only that someone needs to wish her away. Who says there aren't neglectful elven or other magical parents? (We literally know that Jareth has one)