An adventure game can be defined as a game that has the following characteristics:

• It's narrative focused. Not just some narrative tacked on. The narrative is the entire reason someone would be interested in the game. If you removed the story, there would literally not be a game of any kind any more.
• The entire objective of the game is to progress the story to the conclusion. Obstacles that need to be solved to do so are referred to as "puzzles," but these are rarely puzzles in the literal sense but rather just story problems you have to figure out how to solve. Every puzzle solved moves the story along in a tangible way.
• The puzzles are the significant plot points in the story, not things you do outside of the story to arbitrarily block your progress, and not abstracted out to a different kind of activity.
• Lastly, it is not clearly any other kind of game besides an adventure game. If it looks and acts like a... match 3 game, for example, that's the kind of game it is no matter how much it might can be squeezed into the adventure game box with enough mental gymnastics.