Hi,
https://www.openstreetmap.org/way/132647411 is not a riding center, it is just a riding arena. In OSM riding arenas are usually tagged leisure=pitch + sport=equestrian and iD has a preset that sets these tags. Example:
https://www.openstreetmap.org/way/1191712719
See also https://wiki.openstreetmap.org/wiki/How_to_map_a#Riding_centre_(equestrian)