I think the single biggest reason Minecraft has such success is completely accidental, something Notch never consciously caused: Minecraft is a creative game, a game that you need to be creative to enjoy properly, and what do creative people do? They share their creations.
Minecraft came at the perfect time, it came when indie games were becoming more popular, when Youtube video series about video games ("Let's Plays") were rising in popularity and at a time when the internet had become very social, it's so incredibly easy to share content now. If I want 100 people who don't play Minecraft to see a creation I've made in Minecraft it's very easy for me to do that, 5 years ago it would have been close to impossible to do this because the only real place to share content would be the forum for that game, and everyone on that forum would already know about it, so spread of the game would have been severely limited.
Minecraft is a fantastic game and of course if the game was bad it would never have been popular, but the success is in my opinion entirely an accident and a matter of being in the right place at the right time, nothing Notch could ever have expected or intended.