The only time you can take part in this mini game is in Disc 3 with Vivi. You can find Hippaul in the narrow road (connecting the circular area where you can leave Alexandria with the rest of the town). Speak to the lady next to him. This is Hippauls mother and she'll ask Vivi to race with Hippaul to get him healthy. Agree to race with him following the simple instructions. The more you race with Hippaul, the higher his running level becomes. In return you can receive some rare cards and then eventually a key item (Athlete Queen).
Level 10 - Wyerd Card Level 20 - Carrion Worm Card Level 30 - Tantarian Card Level 40 - Armstrong Card Level 50 - Ribbon Card Level 60 - Nova Dragon Card Level 70 - Genji Card Level 80 - Athlete Queen