In Deponia, there's a... hint? system that gets gradually revealed as the player progresses through the game, with cartoon versions of plot points connected flowchart-style. As I play, certain paths get crossed out. Sometimes if I hover over an image, text appears explaining it, but sometimes not. I'm uncertain what the function of this chart is--is it telling me that I made choices that affected the flow of the game? If I replay the game, can I change the outcome? For example, in the diagram below there's an arrow leading from the suitcase (very early in the game) to Elysium (the end of the game) that is crossed out. Could I have done something different to end the game right away?
First of all, I will assume you're talking about Deponia 2. Deponia 1 is linear; there are no alternate endings. However, there are many missable achievements. Overall this 'map' is meant as an impromptu 'todo' list for Rufus. It changes for every chapter in the game, and serves no purpose other than to alert you to locations/actions/etc that exist in each level.
This 'map' has very little impact most of the time, and should serve more as a journal. I know I often ask myself "did I miss something?" when playing these sorts of games. This feature is meant to allow you feedback so you don't get lost in between play sessions.