I've often wondered what it was that made Minecraft fun.
It was frustrating trying to explain it to people who hadn't played it, because I just couldn't put my finger on it. But this review hit the nail on the head.
The reason Minecraft is fun is because it's totally random.
The world generation is random.
When you generate a new world, you're seeing something no one else has ever seen before. Everything is new, nothing is planned. That is why discovering amazing naturally occurring land features is so exciting. There was no artist that sketched this and gave it to a team of graphic designers who built it into the game. This is all new, generated just now, discovered by you. Sure, there are rules that go into the creation of these features, but they are still quite random, and still somewhat rare.
The enemy generation is random.
Enemies generate within certain rules, but their generation is still random. There is no pretense of fairness. When you buy a standard game, and you hit a part that you can't quite get past, you'll keep pushing at it or try a different method, because in the back of your mind, there is the knowledge that a company developed this game, and they did not make it impossible. They probably spent tens of thousands of dollars in testing to make sure it was just the right level of difficulty for the potential buyers. There is no safety net in this game. You are entirely at the mercy of the random number generator and a few simple restrictions.
Resource generation is random.
When I find diamond in Minecraft, I get honestly excited. Because it's rare. Really rare. And when I go mining, I have zero assurance of finding any. I'm not fulfilling a mission to find diamond to continue the main story of the game, where I can be comforted by the knowledge that I will find diamond, because I require it to continue playing. If I find diamond, it's because I used a good mining strategy to find a rare resource, not because someone put an objective marker on my map, and handed me a pick.
The situations you can get yourself into are random.
The combination of the random events occurring randomly on randomly generated landscape can lead to some really random situations. You could be out in the light of day, gathering resources, then fall into a cave filled with monsters, and instantly get overwhelmed and killed. You could be out hunting cows to make some leather armor, when it starts to get dark, and you realize you have no idea where you are or where your shelter is. You could be monster hunting with the best weapons, and the best armor, and take a single hit from a spider, and be pushed off the edge of a heretofore unnoticed cliff. You could be spelunking when a creeper sneaks up on you, jump back, missing most of the blast, and watch helplessly as the sand ceiling collapses, suffocating you.
The world is a beautiful, dangerous, unforgiving place.
Finding diamond, building amazing structures, or simply surviving are all the more rewarding knowing that you did it in a very hostile environment with no safety net or promise of success.
It's just you versus the world, and it feels really good to win.