LOVECRAFTIAN GAMES?
It comes rather naturally that Cthulhu Mythos are an incredible source for game developers, all those eldritch monsters can be used either as enemies, horror elements or parts of the design itself. There is plenty of evident inspiration in games like Bloodborne, Quake, Darkest Dungeon or Amnesia: The Dark Descent, besides those there are video games based directly on the mythology like Call of Cthulhu from 2018 or the games from the Darkness Within series.
HORROR GAMES
It comes rather obvious that the game that basically reinvented the video game horror genre is heavily inspired from Lovecraft's works - I'm talking of course about Amnesia: The Dark Descent. It embodies many of the elements of horror which are the main characteristics of the Lovecraftian Horror. Other titles in this genre that are worth mentioning are aforementioned Call of Cthulhu from 2018, Darkness Within, Darkwood and Alone in the Dark series.
ACTION GAMES
Action games might be the ones which resonate with bigger audience, for people who are familiar with the Dark Souls series - there is one, developed by the same team and set in a bit more Lovecraftian world - Bloodborne. Another game that shouldn't be introduced to anybody is Quake - an FPS only slightly inspired by Lovecraft in it's monster design. Besides those a bit more on the adventure genre side is The Sinking City in which we have to solve a mystery, a common theme in Lovecraft's works.
OTHER GAMES
When it comes to other games that are worth mentioning we have a Roleplaying Strategy game - Darkest Dungeon in which we lead a group of heroes deeper and deeper into a estate filled with enemies in many forms. Other games which share the same aesthetic are Sunless Sea, Call of the Sea and Stygian: Reign Of The Old Ones which is probably one of the closest things when it comes to replicating the feeling Lovecraft works have.