"" If the chess engine suggests the opponent’s move, the claimant wins the game. If not, their opponent wins instead. "" How? Top engine move changes with evaluation time. Longer the wait, better the move.
You can make the engine choice deterministic just by choosing an evaluation time and settings.
Engines can be configured to limit search to a certain depth, which will produce a result after every branch has reached the limit or been pruned. That process will vary in time but be deterministic.
Recent neural based engines tend to not be deterministic, especially if ran multi-threaded.