Visual novel
Also said as VN, Dating sim (a popular kind), Sound novel
A story told in text, over character portraits and backgrounds, with occasional choices that send it down different branches. It promises the depth of a novel, and the sense that you changed how it ended.
It is cheap to make per hour of play and can carry far more story than any 3D game can afford. Branches are the expensive part, because each one is more writing that many readers will never see.
Say it
“Visual novel with three endings and six choices that matter. Track two hidden values, trust and honesty, and show a flowchart after the first ending so people can go back for another route.”
Where you’ve seen it
It is an established form in Japan, with games such as Clannad (2004) and Steins;Gate (2009), whose choices are made by whether you answer your phone. Doki Doki Literature Club! (2017) uses the genre's cute look to set up a horror game.
Not to be confused with walking simulator
A walking simulator tells a story through a place you walk around. A visual novel tells it through words on the screen, with branches you pick.