I think what made Minecraft successful is the fact that you do your own adventure : not a main quest with a lot side quests, not some random main quests selected at the beginning, but your very own adventure. And also because the style of minecraft was very iconic and special (with its cubes, monsters, items ...) and its possibilities (craft).
Before the adventure mode, Minecraft was really really bad for me. I tested it once and I was bored in less than 5 min. There was nothing to do. But the adventure mode changes everything (for my point of view at least).
Of course there is something more subtle in all this at it has been said by Daaark.