It's interesting that once, thinking of a possible model to describe game's objectives,
I drew a similar chart (with circles and arcs, and a similar semantic!).

I like much the way you can easily draw puzzles that you could solve indipendently and switch
from one to another if you get stuck at one of these.

The only thing that I dislike of such approach is the mixing of "figuring out" and "acting",
since usually discovering objectives and achieving them follows opposite directions in the game logic (e.g
"Take the magnet -> Use the magnet on the grate and take the key -> Open the door with the key" vs
"I should open the door -> I should take the key that I saw inside the grate -> I should find something to use to grab the key inside the grate").

Probably I would draw another chart that I would call "Objective Dependency Chart":
- to model just "why" you act and not "what" you do, and exclude from the chart what is merely "acting" (e.g. get the shovel from the sign)
and leaving only what makes you "figure out". For this I would concentrate only on question/problems more than answers/solutions
("Find a shovel" would represent the player's question "where I can find a shovel?");
I would write "acting" steps in a separate chart.
- I would draw it in the reverse order ("Open Basement door" would be the first on the left) and swap the arrows' directions.
The arrow would mean "goal completion depends on the completion of this other goal", but, above all,
"Ok, I would like to achieve this goal... and to do this I just discovered that I should achieve this other goal before").
The chart would describe the new goals that the user would know that has to achieve while playing the game and discovering new informations,
places and characters while trying to figure out to solve more long-term objectives.
Maybe it would help avoiding the creation of "backwards puzzles"? I don't know..
What I'd like is that the chart should help the designer to make long-term and short-term
objectives clear to player in each part of the game.