Unsure if it's a new "type" of puzzle. Virtually any game with multiple characters, buttons and doors plays like this, and can be reduced to a similar graph.
Despite that, I don't want to discourage you. Originality doesn't matter that much. Keep making puzzles like these.
I agree, the title is a little self aggrandizing. As a game designer, I feel it disingenuous to claim it is a "new" kind of puzzle. The person just made a puzzle by adding rules to a set of constraints.
Unsure if it's a new "type" of puzzle. Virtually any game with multiple characters, buttons and doors plays like this, and can be reduced to a similar graph.
Despite that, I don't want to discourage you. Originality doesn't matter that much. Keep making puzzles like these.