Not that it alters your point in any way whatsoever (except to date third party engine-reuse even further), but Hexen used a variant Doom engine, not quake. Hex

Not that it alters your point in any way whatsoever (except to date third party engine-reuse even further), but Hexen used a variant Doom engine, not quake. Hexen 2 was the one that used the Quake Engine.