Are the areas meticulously handcrafted set pieces? If so, that's one sign it could be an adventure game. Is there a fairly involved, well-realized story? Also a sign that it may be an adventure game, but be careful, it could also be an RPG. Are there mind-breaking, often times obnoxiously obtuse puzzles? If so, then it is most certainly an adventure game. The more I play these games now, the more I expect these ingredients to be mixed together.
The problem is that nowadays, the genre seems to have splintered in two directions: traditional point-and-click games, and what feels more like an interactive story. In recent years, we've seen the rise of Telltale Games where their games have been lumped into the adventure game category.
While I do enjoy what Telltale is doing, I have a difficult time really accepting their games as being adventure. The one strong feature that they have is the storytelling. In this regard, the games are great to experience. Good dialogue, well-paced plots, and often with a tasteful amount of humour. As far as their stories go, they're great, but after that I start really questioning whether I should look at what they're doing as adventures.
A lot of the areas don't really feel like set pieces. They're still relatively small, contained areas, but the detail isn't there. There's a certain wow-factor I feel when changing screens to a new area for the first time in point-and-click adventure games that is lacking in the Telltale universe. Going into new zones in King's Quest, The Longest Journey, or even Deponia all manage to impress me with all of the little details that are inserted and it leaves me wanting more as I progress through those games. The lack of detail in Telltale's adventures makes it so I don't feel this in their games.
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All of this isn't to say that I dislike Telltale's games, as I do enjoy them. The stories are usually quite well done, and it's that which keeps me playing them. It's not often that I come across a game with a story that I find as engaging as what they're doing, but this just leads me to look at their games more as interactive stories rather than adventure games. I know it's a biased viewpoint to have, but it is what it is, and I tend to still look at point-and-click as true adventure games instead.