You are correct - this is for case "Sum-of-squares". My apologies, I should have made that clear.

Is it possible that this is the case only if the scoring system is SOS?, because I have calculated the expected changes in GRs a few times in DSS scoring and the GR changes made sense to me (not squared).

The description of Ghost Rating calculations on page https://webdiplomacy.net/ghostRatings.php states:
expectedScore = yourGR / sumOfEachPlayersGR

However in the code, it seems to involve the ratings SQUARED:

$expectedResult[$userID] = $expectedSquare[$userID] / $expectedSum;
where
$expectedSquare[$userID] = $rating * $rating;
and
$expectedSum is the sum of all the players' $expectedSquare values.

My apologies in advance if I am misunderstanding the code.