Hi,
https://www.openstreetmap.org/way/1239464430 and https://www.openstreetmap.org/way/1239464431 are no riding centres (leisure=horse_riding), they are riding arenas. In OSM riding arenas are usually tagged leisure=pitch + sport=equestrian and iD has a separate preset for them.
The riding centre to which these arenas belong can/should be mapped as a sepatare object (area or node) representing the whole centre; this object may then get the tag leisure=horse_riding, examples;
https://www.openstreetmap.org/way/453737341#map=18/53.87989/-2.01987&layers=P
https://www.openstreetmap.org/node/8379284513#map=19/53.66032/-1.86635&layers=P
Sea also
https://wiki.openstreetmap.org/wiki/Tag%3Aleisure%3Dhorse_riding