HI,
https://www.openstreetmap.org/way/1375779944 looks like a building.  Every building should have a building=* tag, otherwise it will not be rendered as a building. If this  building was built for indoor horse riding you can use https://wiki.openstreetmap.org/wiki/Tag:building=riding_hall
The tag leisure=horse_riding (horse riding center) is not meant for buildings, see https://wiki.openstreetmap.org/wiki/DE:Tag:leisure=horse_riding ,