There must be a threshold above which making an engine move is allowed. Because if there's a checkmate move, it will be the best engine move and needs to be allowed.
No; checkmates are not needed. You win the game by almost checkmating the opponent: by leaving them only one legal move, which is thus necessarily the top engine move.
As others have mentioned, that is accounted for in the rules.
My immediate first reaction was also that it would be interesting to have a variant that is the same except you are allowed to checkmate, except then I realized the recursive nature of how board positions are evaluated makes that problematic. For instance, if there's a mate in 2, the first move of the mate in two is now certainly the "best move". Creeping up on a checkmate without ever making the "best move" until the very last one might actually be harder than the win condition based on strangling the opponent described in the current rules.
It just doesn't make sense though for that reason. You can't sneak up on an engine. There's not a single engine out there that wouldn't recognize a mate in 2 moves. Unless the opponent blunders (which actually might be forced if the best defensive move is blocked).
It just seems like you're changing the objective of the game entirely to the point where it's only slightly related to chess.
The article had an illustration of this: the player put their opponent into check where there was only one move to get out of check. The opponent would have to make that move, whether they were human or machine, so the player who made the original move wins the game.
It is an interesting variation on chess given the current state of tournament play, yet it isn't really a solution to the cheating problem since it is effectively a new game with a new end-state. But you are probably right about there needing to be some sort of threshold. While there the rules of the variation says that any move with equal scores is considered equivalent, I would imagine the players would need a very intimate knowledge of how the engine scores moves in certain scenarios.
If you deliver checkmate, you lose. You have to instead force your opponent into a situation where they only have one legal move (which is trivially the best engine move).
You can force the opponent into a position where the only move that saves them is a top engine move. Since they cannot play that move, the other option is to surrender.
So essentially this converts most mates in two into mates in one, but some become ties by repetition.
I don’t see how one way of checkmating could be worse than another way of checkmating? Do some engines give different scores for different check-mating moves? (Different moves from the same position I mean)