How is the game state not just the board state? Move history doesn’t matter in chess (FEN encodes the 50 move rule)

Per Wikipedia, it doesn't encode the threefold repetition rule.

https://en.wikipedia.org/wiki/Forsyth%E2%80%93Edwards_Notati...

Indeed, the 50 move rule, as well as castling rights, whose move it is, and whether any pawns are currently eligible for en passant.

Unfortunately move history does matter

Timing of moves