First problem I saw: You didn't cut your throttle. If you did, you didn't cut it enough. If you were at 0 throttle, you should've been ruddering hard to bleed E. Had you done that right in the first place, you would've been saddled up no problem.
Second: When he dragged you to the deck, he was clearly slower than you. I'm assuming you aren't an idiot and noticed this. Despite being faster, you followed him in the turn, likely going for a shot. Kappa assumed you would do this (as nearly everyone goes for the shot all the time), and to gain an advantage, he needed to show a little tail. You should have simply yo-yo'd after him, which would have slowed you down a bit so that you could follow his turns without giving up your E advantage, and you'd be able to come down inside him.
Third: You didn't use the vertical. At all. You were simply banking left and right trying to get your guns on him - exactly what kappa wanted you to do. Had you approached this better (assuming you still screwed up on the afformentioned first and second problems), you would have ended up in a rolling scissor, with you already in the driver's seat. I'm going to assume you know what a rolling scissor is, how they start, and what to do in one, so I won't go into that.
~rat
edit: the most important thing here was to cut throttle properly. If it were me attacking kappa, I probably would have gotten slower than him on my first pass so that I could get on the same flight path as him, then gone balls to the wall to close in. I don't fly the spit16, so I don't know how quickly it slows down, but that works in the Ki every time. Rudder always helps. Even if you get TOO slow, 99% of the time your target won't notice and will continue turning. Good sticks are included in that 99%.