That is not quite the right calculation. To see this, try plugging 0.75 into the same formula to get Stockfish's expected score. The result is about 0.3545. If this were the correct formula, then the two expected scores should sum to 1, but in this case we only get 0.3612.
Instead, you should convert the 0.25 to "odds" form. 0.25 is 1:3 odds, represented by the number 1/3. (1/3)^((3585 - 2864)/200) is about 0.01905 (still in odds form). To convert this back to an expected score you would take 0.01905 / (1 + 0.01905) = 0.0187. So Magnus Carlsen's expected score is 0.0187.
Applying the same method to Stockfish, we have 3:1 odds, which is represented by the number 3. 3^((3585 - 2864)/200) is about 52.48. Converting back to expected score we get 52.48 / (1 + 52.48) = 0.9813. So Stockfish's expected score is 0.9813.
Our sanity check is to add 0.0187 + 0.9813. The result is 1.0, as it should be.
Instead, you should convert the 0.25 to "odds" form. 0.25 is 1:3 odds, represented by the number 1/3. (1/3)^((3585 - 2864)/200) is about 0.01905 (still in odds form). To convert this back to an expected score you would take 0.01905 / (1 + 0.01905) = 0.0187. So Magnus Carlsen's expected score is 0.0187.
Applying the same method to Stockfish, we have 3:1 odds, which is represented by the number 3. 3^((3585 - 2864)/200) is about 52.48. Converting back to expected score we get 52.48 / (1 + 52.48) = 0.9813. So Stockfish's expected score is 0.9813.
Our sanity check is to add 0.0187 + 0.9813. The result is 1.0, as it should be.