Which member of the Queen's family is a world champion horse rider?

Zara Tindall, a member of the British royal family and the granddaughter of Queen Elizabeth II, is known for her exceptional skills in equestrian sports. In 2006, she achieved significant recognition by winning a gold medal as part of the British team at the World Equestrian Games in Aachen, Germany, specifically in the discipline of Eventing. This accomplishment solidified her status as a world champion in horse riding.

The other options, while notable in their own right, do not have the same level of achievement in equestrian sports. Pippa Middleton is primarily known for her role in the public eye through her sister, Kate Middleton, and for her work in event planning and writing. Princess Eugenie and Kate Middleton have not been recognized as world champions in horse riding, focusing instead on their respective royal duties and personal interests. Thus, Zara Tindall stands out as the clear choice due to her specific accolades in horse riding.