Not all fast-moving action is challenging for a camera and lens' AF system to track. In this case, the horse and rider are circling me. The subject distance is remaining the same regardless of how fast the action is moving.
The 5D III and Tamron 70-200 VC are good for far more challenging subjects, but if what you have to work with is not the fastest and most-accurate available, position yourself to catch the action moving side-to-side.
Camera and Lens Settings
187mm f/2.8 1/1250s
5760 x 3840px