Chess notation is very compact, you don't even need to say where the starting piece was in most cases because it's implied by the move.
If you have 2 rooks on A1 and H1, and the move says rh4, only one of your rooks can legally make that move. However if the move was rc1, both rooks could make that move so you do need to disambiguate.
Now however Niemann is entering the moves, he's got more to type and more places he might make a mistake.
one I thought of is to rank all the squares from most-used to least-used, then assign each of them a Morse code, simplest first. 64 squares is 2^6, so the maximum length input you would ever need is six. given a usage frequency for each of the squares, you could calculate your average input length by the sum of all len(square_code) * square_frequency divided by 64.
assuming all squares are the same frequency (1/64), it's just the sum of all len(square_code) divided by 64, which I believe comes out at 322/64 = 5.03125, although I could be wrong about that.
this makes your maximum necessary input per move 12 bits, but your average will be lower, depending on the frequency distribution of squares. (ignoring castling and en-passant for a moment) this is 2 bits more than using a piece+target square technique
would that same someone be able to pull something like this off on their own, or would they need assistance building/programming/etc? At that point, how many people need to be involved before it becomes a secret too big to keep, or dead bodies start showing up within the cheater's orbit?
yes a cheater could have - for example - a subdermal implant that vibrates to update them with a killer mid-game line to go down, but, without the internet, it would be a huge uphill struggle to update the board with the moves. certainly not impossible, especially if you were very dedicated, but very, very hard to get right, especially without getting caught under such scrutinous circumstances