If you're familiar at all with the Call of Duty games, then you can probably see the relation between FNaF's plot and that of the infamous zombie mode.
That wiki article is rather long, and I don't quite know why it includes the Mob of the Dead map, since it's completely separate from the main storyline, and actually a very solid example of unfolding storytelling, but the jist is rather simple. You start small, but complicate the story further and further as you go along. You just make the whole thing up as you go along, and pretend you had it planned this way from the beginning.
Stories of this nature tend to have drastic tonal mood swings, absurd plot elements, loose continuity, and only seem to get bigger without ever tying themselves back together. It's a bit like a soap opera, or the DC/Marvel comic universes before each reboot: Storylines that exist only to continue into proposed infinity.
But the FNaF/CoD Zombie method has one very important element that differentiates it from comic books. The most important part of these stories is to hide the most important plot elements behind extraordinarily cryptic "easter eggs," and require the community to solve them. The beauty of this method is that the internet has united the world since the 90s, so while these puzzles may be nigh impossible for any given individual to solve, the combined hivemind of the gaming community will figure them all out and summarize them within days.
You look smart, and your fans ignore the ridiculousness of the storyline because they're perplexed by the sheer genius of turning wall tiles into buttons.
And, when what you give them isn't enough, because you're 3cryptic5me, people try to figure the plot out for themselves. The theories start circulating as every individual line of dialogue and continuity error is taken out of context and reinterpreted as a work of high art.
It's a very cheap trick, but it works. You can be a mediocre, or even terrible storyteller, and still create the "unfolding masterpiece" of the millennium just by following these steps.
Of course, if you want to say people only care about FNaF's storyline because the game's already good/scary in its own right, then that's a different discussion. But the story itself is not one that can stand on its own. It's lackluster at best, and uses cheap tricks to fabricate audience investment.