Along those lines, a game that marked in many ways the high-water mark and end of what is now an extinct genre - Grim Fandango. At one time "Adventure Games" were a major share of the market. After Grim Fandango, major studios ceased to make Adventure Games as they seemed to feel that the market wasn't big enough to justify the expense. Adventure Games began to incorporate action/shooter and RPG elements, and action/shooter and RPG games began to do more with cut scenes and carefully plotted storylines. Now you have things like "The Last of Us" and "Uncharted" that have story going but aren't accessible or enjoyable to the gamers that purely enjoyed playing out the story without heavy reliance on combat, reflexes, and so forth.
I would say that genre of games is pretty far from extinct. It's mainly filled by indie developers rather than AAA studios, but it's a fairly rich niche when you get into it. Thimbleweed Park, What Remains of Edith Finch, and The Stanley Parable are the first names that come to mind, along with anything from the Telltale games series.