Hi,
https://www.openstreetmap.org/way/1320461270 and https://www.openstreetmap.org/way/1320461271 are no riding centres, they are riding arenas. In OSM riding arenas are usually tagged leisure=pitch + sport=equestrian; compare https://wiki.openstreetmap.org/wiki/Tag:leisure=horse_riding
They may belong to a riding centre which in this case can be mapped as a separate object (node or area), like here: https://www.openstreetmap.org/way/243744278#map=18/43.676935/11.445329&layers=P