Hi,
https://www.openstreetmap.org/way/1253951029 is not a riding centre (leisure=horse_riding); it is an outdoor riding arena like https://www.openstreetmap.org/way/1026068321. In OSM riding arenas should be tagged leisure=pitch + sport=equestrian and iD has a preset for riding arenas that does that.
Compare https://wiki.openstreetmap.org/wiki/Tag:leisure%3Dhorse_riding
