Just some observations...
I watched the film from the YAK's perspective... It looked to me like he lost sight of you at the point where you two were barrel rolling together. So, it looks like he tried extend to reaquire you. Looking at the quick backward glances while he was running, it appeared that he may have been seeing you AND Agent360 pursuing him. He didn't know that you had called everyone off. If he had taken a longer look backwards he might have realized that Agent360 wasn't really pursuing him. Perhaps the run was partially a product of his quick glancing SA, longer looks might have allowed a better assesment of the situation.
I also noticed that at about the same time that you turned away from the chase, his friend in the P38 who you had shot earlier, showed back up. Were they winging together and he was waiting for his wingman to get back into the fight? Was he trying to suck you into a 2vs1? Hard to say.
He did turn back to you once you broke off. I have seen this kind of behavior quite a bit in the MA. So, I've tried to get into the habit of breaking sooner if it's an enemy that I am not catching fast enough and I think I can beat. By breaking as soon as you realize that you aren't going to run him down, you are offering a new 1vs1. So, maybe if you had turned 90 degrees off the chase sooner, he would have come back sooner. Allowing the 1vs1 that you wanted before he got so close to his home base and his friends.
As for his HO attempt, it was simply a mistake on is part. It shows me that he is probably inexperienced and was not confident that he could beat you in a 1vs1. So he took a shot at you on the merge, hoping to end the fight early. You had out turned him once already, he probably didn't feel like he could beat you in a turn fight. Unfortunately for him, it forced him into the merge nose down. But your first turn after the merge wasn't very aggressive, I think that perhaps you gave up the chance to take advantage of his mistake and kill him right there, giving his P38 buddy more time to get into the fight. Which he did. The 2vs1 forced you defensive, until the P38 was able to knock your wing off.
So, was him running really wrong? In the end it probably turned the tables on you. It sucked you into his territory on the map, away from your own friends. Forced a reset of the fight. You had out turned him once, were on his long six while chasing, but he forced you to allow a new first merge or follow him deeper into Rook airspace. When he did re-engage you, he had a friendly (probably wingman) close by. He and the wingman forced you defensive until the wingman killed you.
Just another way to look at things. I think "Run and HO" is a little too simplistic. There's a lot more that happens in these MA fights. Many more things that must be considered.