Premium Accounts receive additional Honor and Valor for completing Game Arena modes and quests:
Additional 10 points for every Game Arena quest completed.
Additional 10% points for every Game Arena dungeon or PvP game mode completed.
Judging by the rest of the stats, one side had no cleric. So you were probably camping their spawn, and were sometimes inside of the no honor zone. Because of that, some of the kills you got weren't worth anything since you achieved them while inside of the no honor zone.
Pretty much what they said. You also won't get awarded for damage, healing or kills against a target who is in the Honorless zone, even if you were outside of it.