FNAF Shooter takes the animatronic-horror premise and inverts it: instead of hiding behind doors watching cameras, you're armed. The animatronics come alive at night in a supermarket, they've cut the power, and you fight your way through them.
It's a shooter with a horror skin rather than a survival-horror game, and that changes the tension — you can fight back, but ammunition and the dark are still against you.
No — it's a fan-made shooter built on the animatronic-horror premise. The official FNAF games are Scott Cawthon's survival games where you can't fight back.
It's tense rather than terrifying, because you're armed. Jump scares still happen, and headphones make it considerably more effective.
Yes — it runs in the browser with nothing to install.