They mean that you only need board position, you don't need the previous moves that led to that board position.
There are at least a couple of exceptions to that as far as I know.
There are at least a couple of exceptions to that as far as I know.
So... unless I'm understanding something incorrectly, something like "the three last moves plus 17 bits of state" (plus the current board state) should be enough to treat chess as a memoryless process. Doesn't seem like too much to track.
This means you do need to store the last 50 board positions in the worst case. Normally you need to store less because many moves are irreversible (pawns cannot go backwards, pieces cannot be un-captured).