If you can teach your kids how to play chess and keep their cool after YOU WILL HAVE REAL WINNERS IN LIFE...
The reasoning:
Chess is a lot like puzzle solving and a few similar dynamics in life... if you can train your kids (and yourself!) to accept someone else's better puzzle-making then you can literally have more accepting people and a measurably better population in life accepting loss of this kind.
Also people can accept they are not perfect because Chess is not only about death and damage or defeating people or ego. It's about accepting happenings, puzzling and even learning to forget about it while still able to play the next time and not ignore this game (or these deeper and easy-when-you-know parts of life).