The Backgammon Race is unlocked on level 28. The Backgammon Race grants you Race Points for your performance in Contests. Every time you rank in the top 500 of any Contest throughout the duration of the race, you get Race Points.

The more times you rank high in a Contest, the more Race Points you earn.
You get more points when you rank at the top of a Contest.

To checkout from a Race, simply click on the contest tab on the right side of the screen, then select the Race tab at the top right.