Hi,
https://www.openstreetmap.org/way/1329894211 is not a riding centre (leisure=horse_riding); it is an outdoor riding arena like https://www.openstreetmap.org/way/269697395. 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=horse_riding and https://www.openstreetmap.org/changeset/147811585