Scar can't exactly be called whiny for one simple reason: he actually gets up and does something about whatever he doesn't consider "fair". If Scar were whiny, instead of killing Mufasa in order to get the throne, he actually worked towards forwarding the goal of becoming king.
When he's finally king, he's expected to pull miracles and therefore fails on everyone's expectations. Refusing to pick sides, he allowed the Pride Lands to go to ruin for reusing to abandon either the hyenas nor the lion pride, thus angering both parties. Somehow I don't think that he wouldn't complain when everyone are begging everything out of him.