Here now!! Play nice kiddies!
Good answers will usually not be obtained here by referring to people and or posts as "dumbfuck" Pugwash, just so as that you know.
I'm not so sure their is a real technical answer to your question. Pull right and it goes right becaue it changes the shape of the kite, thus causing one side to slow down(stall), which causes the other, faster flying side to fly over the slower wingtip. Pulling right on your control bar is like hitting the brakes on the right side of your kite. Traditionally, 4 line kites have always been flown with handles, allowing more direct control of applying the brakes to the wingtips...you could slow one tip and turn the kite or you could stall both sides at the same time if you wanted. By moving to the control bar method, it's easy to lose focus of how it's working because the front lines come together as one at the bar. It's basically still alot like how the handles work to control the kite except you can only apply the brakes to one side of the kite at a time....aside from a little sheeting action. If you were to take a 4 line kite flown by handles, and attached the handles together as one, end to end, with the front lines closest to center(sorry if that's not real clear), and the brake lines at the ends of your newly formed 'bar',(trying to draw what I mean.... l___l_l___l ...like that) you would have the same effect as we use now with the inflatables except your front lines would come down to the bar side by side as opposed to becoming one, but because they would be so close to the center(pivot point), it would be about as if they were one...you can turn the bar either way, thus applying brakes to one side at a time, which makes for simpler controlling, but you can now only apply the breaks to one side at a time as opposed to the control you had to each side at the same time before you joined the handles into a bar. I hope that some of that rambling added up to something for you.
The way a kite turns can also be relevant to the power it produces while it turns. If one of the kites wingtips stalls to the point of allowing the kite to almost pivot around a point, it will have less power through the turn than a slower turning kite that has some forward speed as it swoops through the turn. This can be seen by flying a foil set up with 4 lines going to 2 handles. If you were to control that kite in such a manner as to make it set and spin in the sky, it would produce significantly less power than it does when it is moving forward through the sky. Most of the lift and pull are generated by the kite moving forward through the sky. So as they achieve the ability to make inflatable kites turn faster, it also becomes important to find the right balance of turning speed and forward movement through the turn to maintain a good constant pull throughout the turn.
I'm pretty sure that I not also strayed from your original subject a little, but I too proabably have failed to give you a suitable answer...but I tried, in the least 'dumbfuck' way that I could. If you really wish to find some aerodynamic explanations of a more technical sort than I have given you, you may have better luck researching paragliders and or parachutes. They have been produced longer and probably have easier to find technical data because of that, than kites do today. And they too are basically kites, and are turned by the same principle of stalling one wingtip.