This is the answer, and it makes all the other answers in this thread seem quaint.
Only game where I routinely stopped and stared at the screen in abject despair at making any progress, or surviving, or saving anyone. And every death makes the game more difficult, and you begin to realize you'll probably never beat it, and if you do all the characters you care about are going to die anyway. Absolutely brutal, and one of the three best games of all time imo
Alien Isolation because it's not a game that you win, it's a game that you endure and survive. Truly fantastic game that helped me cope at the time when I was living under constant stress. It might sound silly that I was trying to cope with stress by playing a really stressful game but oddly enough it worked because at least it gave me some sense of hope that overcoming your difficulties is possible if you're strong and determined enough.
I've always thought Fallout games were half depressing. Its always decrepit buildings and rusty cars everywhere. NPCs live like slobs and the music (1940-50s style) can have a dreary sound to it sometimes.
Hellblade - As people have already mentioned. Senua's world is so sad, bleak and hopeless due to her mental illness. The voices in her head amplify that feeling.
Quantum Break - Time is literally coming to an end and therefore so is the world. The feeling of despair is palpable in this game.
Horizon Zero Dawn - To a lesser extent than Quantum Break it gave me that same feeling of despair and impending doom through the holograms and data pads found in the game recounting the end of the civilization as it occurred in the past.