Double buffering and determinism are not necessarily related. Determinism requires that everything that could affect the execution of logic is captured as part of the input, and (this is the annoying and error-prone part), that anything that is not captured as part of the input does NOT affect execution of logic.

If execution of logic is always performed in the same order, then the partially updated world state is not a problem for determinism (though it may be for correctness). Double buffering may let you reorder the execution of logic in different ways and still keep it deterministic. This would likely be needed for logic that executes in parallel threads, which is increasingly important for high-performance game engines.