For many of the motorized activities such as this one, you need to be 18 to be able to drive the vehicle. The child's price is probably as a passenger. For other excursions that give age limits, many times the age limit is imposed by the cruise line. If you were to book the same excursion on your own directly with a tour company, they can tell you if a younger person can or can not go on the tour. So if you are stuck wanting to do something and the cruise line says no due to age limits, try a web search on the tour and location and see if you can talk directly with a tour vendor about age restrictions. BUT be aware that a tour operator may have his profit from you factored as being more important than your child's safety.
Carnival Cruise Lines:
Fantasy 90, Celebration 95, Victory 05, Conquest 05, Spirit 6/06, Freedom 6/08, Holiday 7/08, Victory 6/09, Valor 9/09, Dream 6/10, Splendor 8/10,Conquest 8/11,Magic 11/11,Triumph 4/12,Spirit 7/12,Freedom 11/12, Triumph 2/13 - The fire cruise
NCL Dream October 2006, RCCL Mariner OTS June 2007, Celebrity Silhouette 2013