Naaa. Minecraft has always had it's own special appeal. I think Ark will be like Minecraft's RPG twin.
Considering ARK only has one attraction towards children, being Dinosaurs, I think the age gap between both games are completely different. Minecraft appeals to all ages, whilst ARK appeals to "older" I think once ARK is completely released next february, it will be a much more popular game than what it is now, I look forward to that, but I doubt it'll do as well as Minecraft has honestly.
If ark keeps going how it is I 100% believe it will pass all other popular survival games. But minecraft is on its own level its nearing the most sold game of all time.
Wasn't there an announcement about a week ago that ark hit 2 million sales? It only being PC and requiring high end hardware is definitely a big limitation.