I think the "How Combat Works" rule on the page explains most of this:
If you MISS or if the enemy is NOT STUNNED, it attacks. So if you do enough damage to stun it, you will skip the enemy attack portion of this round. There's nothing to say you don't continue to Round 2. So regardless of whether you MISS, NOT STUN, or STUN the enemy, you'll still move on to Round 2.
What is wildly unclear to me is the meaning of "if you defeat th enemy" - there is no condition spelled out on the page or in the Combat rules of how to determine defeat. For myself, I'm going to assume that for each round I STUN the enemy, I'll take the gold reward.