The way we solve this problem is not by thinking in term of pure chess logic. We solve it by thinking "what did the puzzle creator thought". So we recall from memory what kind of patterns are suitable for such a problem and start a tree search. It is similar the what a chess AI does but nodes are abstract patterns rather than just chess moves.
This puzzle follows a mental pathway that is common for most humans. We could also design problems that can easily be solved by specific chess AIs but not by humans or other chess AIs : just make it so that the AI naturally moves in the right direction, for example by making specific heuristics always right.
So while this problem is interesting for getting insight into the way humans solve puzzles, it doesn't make the human brain special.