(Edit: didn’t realize Vivienne Dunstan replied while I was typing, so it’s nice she also suggests Eat Me!)
Narrowing it down to non-Lovecraftian and also fantasy-based doesn’t leave very much.
Looking through games tagged horror and games tagged fantasy, I can see:
Eat Me, a dark fairy-tale about a child cursed to devour everything. You’ve probably played this one; if not, it’s one of the most popular if games of the last decade.
The Act of Misdirection, which is a fun game involving magic tricks. It might be more industrial era, but it definitely has fantasy magic elements.
Heretic’s Hope is a complex twine game about a society of human-sized insects dealing with actual humans and having to satisfy their dark gods (less Lovecraftian, more like dark DnD deities).
Hansel et Gretel - La Revanche This one is in French but it’s a really cool Vorple horror game where Hansel et Gretel are monster hunters and have RPG fights.
Ghosterington Night and Hallowmoor - Details are both kind of fun horror, one a simple parser game about chasing around guests at a deadly party and the other a complex twine game with inventory management and spooky enemies like goblins, witches, skeletons, etc.
Carpathian Vampire is an older-school horror game about a vampire.
The Horror of Rylvania is interesting; before Inform came out and after Infocom, TADS was one of the biggest languages to use, and there was a series of games called Unnkulia that were pretty popular. This was the first horror game by those people. There’s a reason it never really took off; this one is infamous for having you examine one specific piece of scenery in one room out of many identical such pieces of scenery.
A lot of Emily Short games like Bronze and Metamorphoses are more fantasy than horror but have unhappy and/or melancholic settings and endings. Plotkin’s The Dreamhold and Hunter, in Darkness are also both fairly grim fantasy games. Similarly, Amanda Walker’s Fairest is a darker retelling of fantasy stories.
A lot of Chooseyourstory games are dark fantasy. They tend towards very dark stories involving rape, incest, racism, torture, etc.