I think Necrum could probably explain why the series is as popular as it is better than I could, but a lot of the reason that people enjoy the game is because of the story. Mainly because FNAF does environmental storytelling really damn well, and I don't think I've seen nearly as much groupthink come out of a title since...ever, really. The various mysteries behind what's happening (and what happened) as well as the implications behind the truth and whether we have all the pieces, it's all really fun stuff.
I will give FNAF credit to that. Similar to games such as Destiny and Dark Souls, FNAF does do an excellent job telling a story through it's environment. I've seen - like probably many others - MatPat's Game Theory on the background and information of the game to help develop plot. However, similar to the other games I mentioned, I think others besides myself may agree that on a first look at the game, people aren't going to really know what the hell is going on besides "oh these animatronics are attacking me, must survive."
You're going to get these hardcore fanatics of the game like MatPat that will help explain what is going on, but personally I don't think that environmental story telling is the best kind of story telling. I'm a huge fan of games like Destiny and Dark Souls, but you won't know what the hell is going on unless you do further research on the game (which I don't really believe is the best strategy in going about explaining your game.) While I think yes, it's a different way to tell the game, I don't think it's the best way to go about it for the masses in general and on a consumer basis.
People generally tend to jump on the jumpscares because they're traditionally cheap and lazy, but I think FNAF (barring the second) use them pretty well by making them a negative sanction and, well, nothing else (though even they tend to give narrative clues). Honestly, I daresay a good part of the fanbase wouldn't even really mind if they were thrown out.
It's true that jumpscares are more integrated into the core gameplay of the game than other games, but I think that's why just personally for myself I hate the concept of it. In general, we're trained and wired to think that in games - and in movies - jump scares are cheap and lazyand a way to mask an entity as being classified as part of the "horror" genre. When I think of games such as P.T. and certain scenes/events in Dead Space, I get a more definitive idea of "horror" based on the story telling and buildups. Sure, there are instances of jump scares in these games, but I think of these as true horror games more than FNAF. But that's just
A GAME THEORY my personal preference and could be debated as to whether those games are true horror games too. It's a tricky line to walk essentially is a hard concept to master.
And as far as it being essentially the same game...well, I guess this depends on the person. It changes things up more than CoD did back in its rehash hayday and Pokemon did prior to XY, plus it's pretty cheap- but it's also pretty short and you won't spend days on it. So it's a total two-way street, there.
Which is also why I stopped playing Call of Duty and Pokemon, as well as games like Assassin's Creed awhile back cause it's the same thing over and over again haha :P I like new, intuitive games than the same game reskinned. I think more over the issue with all of these examples including FNAF but excluding Pokemon - I'll explain why in a sec - is that they are consistently released in too short of a window. The creator of FNAF released 4 games over the course of 1 year; Call of Duty and Assassin's Creed releases a game every year. This in turn oversaturates and diminishes the quality of the game in my opinion, as you are getting the same thing over and over
and over again - it doesn't
really add too much to the formula and is why gamers like myself get tired of the same thing and feel meh about the game. The reason why I give Pokemon a semi-pass and is an exception is because the core game series isn't released on an annual basis, but there is still argument that the game formula is stale (which is why I stopped playing after Platinum.)