For those who haven't heard of Threes, I highly recommend giving it a try. It's the original game that 1024, 2048 etc were cloned from (and I think it's still the best by far). Wikipedia has a good summary: https://en.wikipedia.org/wiki/Threes#Legacy
It's with 2048 that I actually got hooked, it felt like a more natural and seamless game to play. I think it's the simplicity (no cuteness, no craftyness) that helps abstract the game, and of course dealing with powers of two makes it all the more natural. It felt a lot easier to get in and out of the game, be it for 30 sec to check the train station or 4 hours until lunch break.
I feel like Threes was the cute and whimsical game, while 2048 could probably become the classic game, in the same kind of spot as Tetris.