I think that makes him Chaotic Good. While he’s an incarnation of the Balance, the actual Eternal Champion doesn’t have to be of the Balance themselves (that wouldn’t be helpful in times of excessive Law or Chaos) - he’s a Chaotic incarnation vs say Corum or Hawkmoon, who I’d characterize as more Lawful.
Elric lives in a time when the forces of Chaos represented by Melnibone and Pan Tang are actually in decline, and the more Lawful human Young Kingdoms are on the rise, so it is understandable the Balance calls a Chaotic champion.