building=gatehouse might be an option, though not 100% matching this one.
https://wiki.openstreetmap.org/wiki/Tag:building%3Dgatehouse

Don’t bother if you cannot solve all "quests" in StreetComplete.  It used to be a nice app but they keep adding new quests, to the point that it becomes silly at times; some quests can be ignored entirely and leaving building=yes is not a problem.