Do you mean a Lovecraftian game or a Lovecraft themed game? Because there is scarce of the former and abundance of the latter.
Most games miss the point of the stories pretty hard, and Dark Corners of The Earth is one of those.
Has this video not been posted yet? https://www.youtube.com/watch?v=7DyRxlvM9VM
They talk about common problems with Cthulhu games, and how they'd design one that really stays true to the mythos and brings it to life properly. The conclusion seems to be that no one has really managed this yet, but they mention some good horror games that accomplish something similar.
It doesn't really matter if the stories/creatures in the game are from an actual Lovecraft novel; the most important point is the atmosphere: the mystery, the horror, the horrible discoveries leading to insanity... I know it's not really possible to have all of this in a game, but that's the main point.
Well, anyway, thank you for all the suggestions; I have a lot of stuff to try now!
Plus... Lovecraft's stories very often don't meet the mark the video sets out there.
Hell, even Call of Cthulhu ends with the world not-destroyed or irreversibly changed beyond recognition - Cthulhu is again asleep at R'lyeh, a bunch of cultists got killed or arrested a while ago, some of the sailors survived...
And that's not going into stories like TCCoCDW, Shadow over Innsmouth or Dunwhich Horror, where the local threat is defeated - perhaps it's not ol' Facetacles or Goldenballs himself, but the local supernatural threat is neutralized, and in one of the above the government is made aware of the threat by credible sources.