In the 9-stone handicap game, if Black wins then Black gains 3.78 points, otherwise Black loses 20.21 points. This is fair if
(Black’s probability of winning)/(Black’s probability of losing) = 20.21/3.78 = 5.34, i.e. Black’s winrate is 84%. This is unrealistic since the link you pointed to says that Black’s winrate is less than 50%.