I could be completely wrong, but when I hear this I always think of the eminem song "Stan", which he raps about this crazy fan named Stan.
Stan is eminem's self-proclaimed "biggest fan" and so fanatically devoted to the rapper that he eventually kills himself just because eminem didn't write back to him in time after Stan reached out to him a couple of times.
So then, fans of players who are over-devoted to the player are therefore referred to as "Stans".
I'm old AF though so I'm probably incorrect.