Many cellphone plans nowadays come with unlimited SMSs.
Two people who with to play chess start Chess App on their cellphone. These two Chess apps running on two cellphones send each other, their own chess moves via simple SMS text.
Ex. a typical SMS text would be "4A->6F"
After receiving SMSs,
the apps will update their screen accordingly.
By using group SMS facility, a spectators group spread all over world, would be able to watch the game live on their cellphones.
No internet connection required here, but just simple old SMS.
Since this is a totally connectionless technique, it will not hold up the telephone infrastructure for the period of game being played.