I never see Eternal Darkness: Sanity's Requiem on these Lovectaftian game lists, but it was so good! The controls kinda sucked from what I can recall, but I loved the fourth-wall-breaking antics that began occurring when your sanity meter dropped too far and brought into question the player's own sanity.
Eternal Darkness is still one of my favorites. Tank controls didn't age well, but (imo) doesn't distract from the unique experience this game offers.
If you play on Dolphin I highly recommend the HD texture pack (https://forums.dolphin-emu.org/Thread-eternal-darkness-hd)
Both The Thing (1982) and Alien (1979) if taken as stand alone works and not viewed with the hindsight of any later added material are very Lovecraftian. Not just in vibe and surface aesthetic, but in the central mythos thesis that learning more about the universe and scratching away at the sleeping secrets never ends well for humanity.
For gaming, I'd add Stasis and Stasis: Bone Totem (shudder especially Bone Totem) to games that follow the central themes of Lovecraft without explicitly placing themselves in the mythos.
Would love a proper Color Out of Space that is true to the original and set in the proper time period. The Nicholas Cage one is a fucking joke, and I had come fresh off of the original story when I had seen it.
My dream production would be an anthology series of Lovecraft's work, as true to the source material as they can possibly be. Doesn't matter if they're only 30 minute episodes.