I disagree, a game being classified as "adventure" tells you that it's not a sports game, a racing game, a puzzle game, etc, so the word as a category isn't
totally useless.
Maybe we should consider things like movie genres to help narrow down some ways that these genre names are used in our localities. For me, an action movie would be something with lots of kinetic energy, so lots of stunts, running around, the characters thinking quickly, and things generally moving along with a more rapid pace. An adventure movie would be something like LoTR, where the focus is much more on lore, plotlines, dialogue, and the overall journey the characters go on.
It's only when you introduce the concept of player input that anyone gets confused about what constitutes an adventure or not, so maybe that's the goal of this exercise; to consider "adventure" as a category which implies some storytelling and environmental elements, but not how the player interacts with the game.
So, maybe an action game is more about the physical stunts you perform to fulfill the quest, and an adventure game is more about the sequence of events you set into motion to fulfill the quest.
About the word "quest", I always saw it as the "current objective" mechanic. So a game might have multiple quests you choose from, or it might just have one. Use of the word "quest" as a genre would be unfamiliar to me, but nonetheless I don't have objections about using it to refer to games similar to the Sierra classics. (Though, I always called those "point and click adventures")