Notifications are a core part of Facebook but the number of users that want game notifications is pretty small as the linked article described (5% acceptance rate two years ago and going down from that). The explicit gamification in this article is pretty disgusting.
Opting out of third-party apps does not affect notifications TMK. At least I still get them, though I don't know if there would be more if I had apps enabled.
Notifications are a core part of Facebook. It's like complaining that Twitter doesn't have an option to stop people retweeting you.