I love rules. If I had to define an atomic unit of what makes a game a game, I'd offer up the concept of rules. Rules are the building blocks which developers use to create unique games. Rules are integral to each and every game, even when not as obviously defined to the player.
The interesting thing about rules is they don't make a game fun. You don't look at a bunch of rules and think "Yes, this looks fun." No, instead you would contemplate what interactions come from these rules and analyze a game from there. What is the player doing? Is that fun? Rules are the medium from which fun is drawn from: they help create the fun interactions inside the game.
The cool thing about rules is that at the end of the day, they are unnecessary for fun. Humans can have fun without rules. But constraints frequently make things easier. And it's the same for interactive entertainment. Rules are like a guide for how to get to a fun experience more easily. Here's a great analogy from Improv Comedy, that I think beautifully applies to video games as well.
“Rules are like landing gear: you need them to take off. You need them to land. But you don’t need them to fly.”
A perfect example of this in effect is an sandbox game like Grand Theft Auto. As in all games, GTA has rules. A weapon does this, a car drives likes this, cops chase you if you break the law, and so on. Simple, obvious rules that mimic real life. At the beginning of the game, players pay attention to these rules. They learn them and it influences their play. But what video games offer apart from any other rule-based game medium (like board games) is that players don't have to consider the rules. They don't even have to remember them. As long as they are aware that they exist, a player may play the game implicitly. Once a player understands this, from that point on, a game like GTA still has rules, they just don't need to be considered by the player anymore. And why should they? If the rules get the player to have fun, it's unnecessary for the player to keep them all in mind.
Granted, plenty of games require players to consider and analyze rules constantly. Strategy games, for example. But the beauty of rules in video games is they are always there, with or without player consideration. Which can lead players to two different wonderful places: discovering new rules by experimentation, and forgetting about the rules and just having fun. This is one of the many unique aspects of this medium.