I always assumed it was because your frame of reference gets longer and longer. For a 5 year old, a day is 1/1825 of their entire life, whereas for a 50-year-old it's a smaller piece of your life by a factor of 10.
Instead, I've always suspected it is novelty and memory. To a 5-year-old almost everything is new and novel, and his memory is absorbing absurd amounts of information each day. If he finds, say, a bottle opener and has never seen one before, it might fascinate him. He might spend 30 minutes just playing with it, turning it in his hand, pondering what it is for, etc. Then he'll remember all the little lessons he learned from it. (He might even think more about it later.)
You, on the other hand, have seen so many bottle openers that you've got a sort of platonic ideal of it inside your mind. You see it and don't even have to consciously think about it. You might not even remember later that you saw it, where you saw it, what color it was, or anything about it.
So my take has always been along the lines that a 5-year-old's experience is filled with brand new interactions with the world, so each day in memory is 'bigger'. We older folks have been there, done that, so the list of things we find important enough to remember is a lot smaller. Most of our "time" is just gone.
You are saying Time slows when you are having fun, I suspect your conclusion is incorrect
I think the perception of time is the rate of change of your brain state. Intuitively, this makes sense-- if I double the rate of your neurological activity, the world will seem to move half as fast. Similarly, if I freeze the activity of your brain and resume it some time later, you'd perceive no time to have passed.
But I think it also applies on longer timescales, too, and to variations in the rate and degree the brain transforms itself-- If you repeat the same thing every day, your brain changes little, and those identical, indistinguishable experiences collapse onto each other in your brain's compressed representation. That is to say, if each week of your life is the same, the situation approaches one where I took your beginning-of-the-week brain state and transplanted to the end of the week without any changes. I should predict that under that circumstance you would not experience the passage of time.
On the other hand, learning and experiencing dramatically new things forces your brain to change substantially, and the kind of cognitive delta that would normally occur over weeks or months of experiential stasis can happen in days or hours.
Once people leave school, many years of routine can go by without many clear perceptual markers. I am noticing this in myself, and it's become a nontrivial motivator for making substantial life changes.
Compounding this is the fact that neurology slows down as we age. I recall seeing a chart that suggested that a 60 or 70 year old will have roughly half (? maybe worse) the reaction time of a 20 year old. That suggests that 8 hours for a 20 year old would feel like 4 hours to a 70 year old. The study did not examine children under 18, but extrapolating the trend would suggest that children's brains are substantially faster still. Perhaps an hour for a young child is neurologically equivalent to 4 or 5 hours for a middle aged adult.
The issue I have with it is that you are essentially plotting an inverse function and it breaks down at age zero.
You can use tricks like quantization (a common one: you only consider whole years), add some constant, etc... but then, it stops being an simple and elegant idea.
Now I think the passage of time is complex and messy subject. We have things our body can use as time bases: heartbeat, brain waves, the laws of motion, day/night cycle, winter/summer cycle, music / rhythmic sounds, the amount of data we have as we recall past events, etc... It can't be simple. The paper points out one factor: the fact that our body functions slow down as we age, but it can't be the only reason.
I also dont have perfect recall but even if I did, at any one moment I am only referencing memories from the same amount of past moments (or at most slightly more).
I really wonder how much more differently than me do you process everything, think, and perceive for this to ring true rather than a pretty but obviously false story.
Take a summer off and travel to unknown lands, and when you get back tell me that didn't feel just as long or even longer than summer break did in grade school. Spend that same summer in the office or in your normal routine and it will fly by.