Remember that The Hunger Games was conceived during the Bush years, back when the left was fearful of big "fascist" government. Their panic drove them to make several dystopian movies like V for Vendetta and Children of Men that expressed that fear. All had an oppressive right-wing government as the bad guy. The Hunger Games is part of the same pattern.
Groan. It’s a totalitarian government. Doesn’t matter whether it’s “right” or “left” wing, it’s the violent subjugation of all others to the service and pleasure of a central tyrannical power. When freedom is crushed, neither “left” nor “right” are laudable positions for the oppressor.