I don’t think that „classic Adventure game“ is hard to define at all, in fact I think it is possibly the easiest thing ever since even the initial KickStarter video itself included all the references you could possibly need (if it didn’t, just imagine the most popular games in the genre which usually come down to LucasArts and SIERRA anyway with some other contenders like AdventureSoft):
0:37 – Grim Fandango (also notice the posters afterwards – Grim Fandango, The Secret of Monkey Island, Day of the Tentacle, Full Throttle)
1:32 – Maniac Mansion, The Secret of Monkey Island
2:28 – Depicted are again Day of the Tentacle, Full Throttle, Grim Fandango
3:20 – Old-school Adventure feature
As for defining Adventure games, they are usually a Mix of story, puzzles, characters and writing as the cornerstones of the genre.
Wikipedia describes it as:
http://en.wikipedia.org/wiki/Adventure_game
An adventure game is a video game in which the player assumes the role of protagonist in an interactive story driven by exploration and puzzle-solving. The genre’s focus on story allows it to draw heavily from other narrative-based media such as literature and film, encompassing a wide variety of literary genres. Nearly all adventure games (text and graphic) are designed for a single player, since this emphasis on story and character makes multi-player design difficult.
Graphic adventures largely developed from Text adventures, there is a short “documentary” of sorts exploring this and the growth of the genre, although the fifth part is lacking:
The term was largely coined and popularized by the first King’s Quest in 1984:
http://en.wikipedia.org/wiki/List_of_graphic_adventure_games
There are various sub-genres, most notably
Puzzle Adventures or First Person Adventure/Puzzle games that have largely arisen from Myst (which kind of created the genre) and encompass titles like Portal, Dream, Homesick, Montague’s Mount, Obduction, Ether One, Kairo, The Witness, XING and so on today. I’d find it very hard to describe many of these as “classic Adventure games”. They often sacrifice story and characterization in favor of puzzles.
The second note-worthy sub-genre are
Interactive movies and FMV (full motion video) games that have largely started with Dragon’s Lair in 1983 and got especially popular through the 90s with titles released on CD-ROMs:
http://en.wikipedia.org/wiki/List_of_interactive_movies
There are still some games produced today like Heavy Rain, Beyond: Two Souls or even The Walking Dead games that loosely fit this sub-genre. They often sacrifice puzzles in favor of story and characters.
The third is “
Action Adventure”, which is kind of a broad term of games that generally combine things like inventory and puzzles but largely focus on Action gameplay, the primary example being “Tomb Raider”. A lot of Adventure games like say Broken Sword or Alone in the Dark tried to go and “evolve” in this direction through the 00s:
http://en.wikipedia.org/wiki/Action-adventure_game
In regards to Broken Age, I’d say it definitely fits the definition of an “Adventure game”, but it is more an “Adventure game Lite” with a focus on the Casual and tablet market similar to titles like Botanicula, Machinarium, Kentucky Route Zero, Superbrothers: Sword & Sworcery which Tim specifically called out as inspiration and doesn’t have all that much in common with the “classics” as many people hoped it would:
http://www.gamespot.com/videos/broken-age-rethinking-a-classic-genre-for-the-mode/2300-6415966/
They even have “Casual” as a genre descriptor on the Steam store and I don’t think they did that as a mistake:
http://store.steampowered.com/app/232790/