Hi,
You have tagged the building leisure=horse_riding but each building should have a building tag, otherwise it will not be rendered as a building on the maps. If the building is an indoor arena you can use building=riding_hall and the iD editor has a preset for that.
The tag leisure=horse_riding is for complete riding centres (and not for buildings). In this case the riding centre seems to be https://www.facebook.com/p/Chiverton-Riding-Centre-100056007231652/. I would recommend to map it with a separate object (area or node), e.g. like https://www.openstreetmap.org/way/1008067851 (Eccleston Equestrian Centre or https://www.openstreetmap.org/node/4920681807 (Eborlands Equestrian Centre)