Fun with Chess is an iOS app that is a nice match for kids wanting to learn how to play one of the world's greatest games. It is not a typical chess experience, because it adds in factors of luck which limits your piece's moves with a roll of the dice.
The game keeps score, so you can play another person and decide a winner at any time. You can play the computer, another person face-to-face or remotely. There is a built-in chess tutorial, and a linked video with more information.
To make Fun with Chess more appealing to beginners, games are limited to six pieces and six applicable rules. I suppose one could complain that this is a chess variant, rather than a standard game, but I think it is less intimidating to someone just starting out, and a good way to learn the rules.