Out of boredom, I decided to make an analysis of the mechanics of the first game. I may do this for the other two games. I will try to have as little bias as possible, and visuals will not affect this analysis unless it does noticeably affect gameplay.
First, I will give a quick description of the mechanic, then evaluate the three main points of them, which are:
Creativity - Pretty obvious, looks at how unique and original the mechanic is.
Significance - How crucial it is to the game, and how much more fun/scary it makes the game.
Logic - How well the mechanic fits into the lore and how logical it is to have it.
For some, I may give some comments at the end, perhaps how to improve the mechanic or some other notes.
I will rate them out of 5 for each point and an overall rating at the end of their analysis.
Music Box (Po)
The music box is a very simple mechanic, introduced to you very early into the game. You are required to keep the music box going by winding it up constantly, for leaving it alone too long will result in a quick game over. You will have to view a certain camera and hold down the space bar to wind it up.
Creativity - It's a "music box" mechanic. The creativity is very low with this mechanic, as it is straight from FNaF 2. This mechanic doesn't have very much unique to it, other than the space bar part of it.
Significance - It's quite a significant mechanic in the game. You'll have to spend a lot of time on it, as it goes down quickly. It's a good way of increasing tension as it makes the player anxious about the music box running out when taking care of other things and about the other things when spending time on the music box. It gives the player something to do in free time, so they don't get as bored. Without this mechanic, the game would be quite boring and much too easy, with the other mechanics going around quite slowly in comparison.
Logic - This isn't explained too far in-game, however, it works, but some spaces will have to be filled in by the player. According to the first night phone call, the music box will prevent Po from moving. Not much more explanation is given by the first night phone call, but it is clear that Po has no eyes and cannot see, depending on sound to navigate. A full explanation can be gathered, as I have made one here: When the music box is playing, Po cannot hear the other rooms, and so, she stays in her room thinking that there is nothing going on in the other rooms. Without the music box, Po can hear the player moving and doing things in the office, so she moves to there. Although one can explain how the music box helps, it would be a bit weird to have a music box there in the first place, and the phone call emphasizing it so much will seem strange, however the music box mechanic can fit in without plot holes, since it's explained how they know that it works.
C = * 1/5
S = **** 4/5
L = *** 3/5
O = ** 2/5
Extra Comments: While the space bar part is unique, it does make winding much easier, and as a result, less tense, as you could hold down the button all of the time and you'd only need to switch to the camera for a bit of time. It's a sacrifice of significance for creativity, so removing the feature would not be bad or good.
Left Door (Laa-Laa/Dipsy)
The Left Door is a simple mechanic, where if an enemy is spotted in the Left Door camera, a button must be pressed to close the door until the enemy leaves to avoid a game over. The reason you cannot keep the door closed is because it has a limited total amount of time it can stay closed until it can be closed no more, leaving you helpless against any enemies that may come there.
Creativity - It's a "door" mechanic. There's not much creative with this mechanic aside from having a door camera instead of a light, having it's own separate power, and having only one door to take care of.
Significance - It's pretty significant, giving you another task to take care of. You'll have to put more thought into using the door, as it's limited, and you'll also want to constantly check the door camera as you won't have much time before whatever's there gets through the doorway, meaning you'll spend quite a bit of time making sure nobody's there. It increases tension as the power starts going down, and when there's someone who just won't go away, you'll be quite nervous about if you'll be able to last long enough before they get in and leave you at the mercy of the other one. It gives you more to do other than look at one character and winding a music box, so it is significant in making the game not as boring, especially early on.
Logic - You can't really go wrong with a door mechanic on this one. You'd use it in real life to make sure someone dangerous won't get through. However, it has the same logic flaws as the base FNaF 1 doors, as they should use power to stay open when it goes the other way, though that could be passed off for safety, to not get trapped in an emergency. It's not explained why the door and only the door has limited power, though it could be explained by budget cuts, the same reason why you don't have a right door. The door camera does make sense, however. One big plot hole though, is the fact that some of the characters only go through the left door. There is no explanation why they do so.
C = ** 2/5
S = **** 4/5
L = *** 3/5
O = *** 3/5
Extra Comments: There is one flaw with the door camera, and that is the fact that it makes it so you'd do best just staying on the cameras almost all of the time. A door light may be better, requiring you to look away from the other mechanics to take care of another crucial one. However, just like the suggestion for the last mechanic, the door camera is sacrificing significance for creativity.
Tinky Winky has his own mechanic, which doesn't require any special buttons or anything. You are required to look at him on the cameras to stop him from moving. If he manages to enter your office, he will attack the next time you pull up your monitor. His static signifies his location in the office and in the blind camera.
Creativity - It is not directly copied off of any other mechanic, however it does have a large relation to Foxy and Freddy in FNaF 1, due to the fact that they cannot move when watched. The difference here is that watching them is required, as there is no secondary way to stop him, and you have more opportunity to catch him before he moves again.
Significance - Unlike the other mechanics, this one is not very significant, due to the fact that he starts in a room that you are required to constantly look at anyways, and the fact that he is quite slow. He gives a bit of tension when he finally leaves the starting room and when he moves again, but it's not very hard to flip by that camera quickly. He doesn't give much to gameplay overall, and it's actually quite difficult to die specifically to him.
Logic - His mechanic is explained in whole, as a simple malfunction in the first night phone call. Cameras are required for the job anyways, and the malfunction is simply just that. No plot holes here.
C = *** 3/5
S = ** 2/5
L = **** 4/5
O = *** 3/5
Extra Comments: It would likely improve this mechanic to place him away from the music box room and make him a bit more active overall, to make him a bigger threat and increase tension and the amount of things to do, making it more fun.
The fume mechanic is a special one, and is the last one I'll discuss here. It is used to fend off Dipsy, as the Left Door will not actually make him move away. This will allow you to save your door power for Laa-Laa instead. The fume, if used at just the right time, will prevent Dipsy from moving forward. To use, you must go to the first Dining Room camera and click the button. However, you have a randomized amount of clicks before the fume runs out and you can no longer use it, leaving you to waste the rest of the door power on Dipsy when he arrives.
Creativity - This is likely the most creative mechanic out of them all. Instead of requiring quick reflexes and fast action, it requires thought and precision. It does not have a direct relation to any other mechanic (that I know of). It is very creative, and is quite different from anything else we've seen.
Significance - This mechanic is quite significant, as it is the only consistent way of keeping Dipsy at bay. Like the door, tension will rise when it gets low, and when you get unlucky and use a lot of fume in one click. It gives another task to take care of, and it makes you have to think about when you should click it, making gameplay more interesting and fun. The game would be a bit boring with the main mechanics just being a door and a music box.
Logic - Like Tinky Winky's mechanic, the fume is explained completely. Dipsy having better smell to get ingredients to put into the custard machine, and the fume luring him away due to that fact, as well as why Dipsy drains power. However, there is a plot hole. Why doesn't he move back to the Dining Room, since that's where the fumes come from? While this differentiates the mechanic from FNaF 3's audio devices, it creates a plot hole, sacrificing logic for creativity.
C = **** 4/5
S = **** 4/5
L = *** 3/5
O = **** 4/5
Extra Comments: The game could be more exciting and tense if the fume button was moved to in the office, as, like the door camera, having the button in the cameras makes the player want to stay in the cameras almost all of the time. Having to put down the camera, making you unable to quickly get back to the door camera and the music box, can raise tension. However, I would say that this would be beneficial to do.
Music Box = 2/5
Left Door = 3/5
Tinky Winky = 3/5
Fume = 4/5
So those are my analyses of the FNaTL mechanics. If there are any errors, point them out, and if you would like to put in some points of your own, feel free to say them! If you would like more of these, please say so! If you have some analyses of your own, please post them, but don't copy, as I would like to see other opinions on them.