The monsters and bosses you encounter during the Hidden Path quest do not grant FG cult reputation, even though they are marked as ‘Eldritch’. Normal monsters usually have a type before eldritch, such as ‘insectoid - eldritch’ or ‘beast - eldritch’. The bosses (e.g. Guardian of Solael) are only marked as eldritch. I am not sure if this is intended or an oversight (since the Hidden Path is from way before FG).
Update: FG monsters like Stone Gryphons are marked as ‘Construct - Eldritch’, and they do give rep.
The type of an enemy is different from the faction they belong to.
The enemies in the hidden path are classified as eldritch, but they belong to the Beast faction. The Eldritch Horror faction refers mostly to Korvaak’s followers and the like.