HHQ1: Fighter's Challenge is centered in the village of Sturnheim. Is Sturnheim a village that exists in any published (A)D&D campaign worlds, or is it just floating out in the void? There's nothing I can see mentioned in HHQ1 itself, but I don't have (access to) any of the 2e published settings.
It's just floating out in the void, ready to be dropped into a DM's existing setting or serve as a seed out of which a home campaign will grow.
Fighter's Challenge was published at a time when, if an adventure wasn't explicitly marked as being part of a particular setting's line, they were free-floating and generic enough to be fit in anywhere. This was most obvious in Dungeon magazine where there would be a pile of generic adventures and a selection of adventures that loudly called out being set in the Realms, Greyhawk, Spelljammer, or what-have-you, but it was true of all published material in the 2e era, whether adventures or fluff-filled supplements. There was no such thing as a “generic” shared setting to set adventures in, unlike 4e's Points of Light meta-setting.