He said he controlled Sterben up to this point, but decided he wanted to do the actual killing this time. He's the one who leveled the Sterben and was playing DeathGun in-game when the blue-haired guy was killed in the beginning.
Arguably, you could even say that Kirito could have lost if the actual guy was playing instead of wanting to creep on Shino IRL, since it was his actual equipment.
I guess the next question is if the Amusphere tech allows someone else to play as someone else's character.