Funtime Freddy having a Hand Puppet of Bonnie may very well have been inspired by a common interpretation of fixed Mangle (AKA Funtime Foxy) before the release of FNaF World. Fans believed that Mangle's second endoskeleton head was a Hand Puppet of the original Foxy. On the same hand, no less!
While we're on the subject of Mangle, Funtime Foxy's design in this game certainly does resemble a more detailed version of how fans commonly drew fixed Mangle before their full body was revealed.
Likewise, Funtime Freddy refers to his handpuppet as 'Bon-Bon', which is a Fan Nickname for both Classic and Toy Bonnie. Funtime Freddy also has an Electronic Speech Impediment with his stuttering dialogue; often the older animatronics were given similar auditory glitches when fans produced voice-acted content.
Funtime Freddy's voice also, ironically enough, bears a resemblance to the common fan-interpretation of Bonnie's voice.
The game involves giving the animatronics electrical shocks to make sure they're active and working; that includes Baby. Sadly, you don't get to wake the baby.
A few gameplay elements appear to be borrowed from numerous fan games. Notably, the flash beacon on Night 3 is reminiscent of the Camera Flash from Five Nights at Candy's 2, and hiding under the desk in Baby's room appears to be taken from the same hiding mechanic as Five Nights at Treasure Island.
Perhaps unintentionally, but on a darker note, just as in Popgoes, the backstory revolves around the accidental murder of a major character's daughter, in this case William Afton.
Rockstar Foxy has a higher Entertainment value than the other Rockstar animatronics based off the main quartet. Rather appropriate, since Foxy was always the fan favorite.
One of the animatronics you find as salvage is Springtrap. During the buildup to FNaF 3, one of the speculated names for him was "Salvage", since he was first seen looking over a box of animatronic parts, pondering "What can we use?"
Three joke updates Scott made on April Fool's Day during development of Ultimate Custom Night poked fun at three notoriously contentious (and discredited) fan theories — "Foxy is a good guy" (Foxy aids the player in different ways), "Phone Guy is Purple Guy" (Phone Guy calls except when Springtrap is present; he can't be in two places at once), and "the entire franchise is All Just a Dream" (Nightmare Freddy is disabled via an alarm clock that wakes up the player).
