The reason for me is simple – gadgets and online presence wreak havoc on an ability to focus and concentrate. I miss childhood days when I could get lost in a book for a good half a day.
So this "no e-books" policy kinda ruined the analogy for me (I would love to have such a cafe nearby, but where I can read). But I get that it's not that easy to tell if it's a tablet or an e-book, and many e-books have browsers and the internet and a full-fledged Linux box inside, so there is no easy way to draw a line.
What's the broader idea behind No Screens Cafe? The article does a good job of describing the rules but not explaining the reasoning behind them.