I'm not 100% sure on this but:
If you did enough damage in the first round to STUN them, you should get the gold reward and they are defeated. It seems like under normal combat, the enemy would DIE, but this particular combat requires them to be STUNNED (they may be used tomorrow)
Therefore you should not play the 2nd round of combat. (but even if you did, I think because the enemy is STUNNED, they wouldn't be able to attack you)