What Remains of Edith Finch (Giant Sparrow, 2017) has a part of the games that uses photography mechanics as part of the gameplay. Focusing and taking a picture at the correct subject triggers the story to move forward.
Note: video below is a walkthrough and contains spoilers of the game.
UFO: A Day In The Life (Love-de-Lic, 1999)
the player must use a device called “COSMIC,” a kind of camera, to reveal the creatures. Once a certain number of photographs have been taken, the player character returns to the ship to develop the pictures. This is done by giving the negatives to a giant floating head called “Mother.” As more aliens are rescued, more areas open up and different times of day are available for exploration.
Michigan : Report from Hell (Grasshopper Manifacture, 2004)
As part of a three-man news crew from Zara Television it is your job to report on the drama as it occurs. Your role in proceedings is passive, and one almost like a director observing his cast and crew. […] But you do not merely sit back and watch colleagues fighting for their lives. Capturing the action is part of the game, but by searching rooms and environments you can identify potentially life saving (or puzzle solving) items by zooming in on them. Failure to do so may result in another path being taken, or at worse your female reporter dying in a gruesome encounter.
The Amazon Trail (MECC, 1993) is an educational game where you play a naturalist taking and identifying photos of all plants and animals you encounter in the journey.
Lumen is a platform-puzzle video game where the player assumes control of a girl trapped in a world of nightmare as she tries to make her escape. With the sole help of her camera, she will have to dodge traps, run away from her enemies and use her photographs to change the world that surrounds her.
Dark Clouds 2 is a PlayStation 2 game where photography is both part of the game mechanics as well as an extra feature to offer free photo taking opportunities.
Some pictures will add points to the game and will increase the character’s “photography level”.