Even if you are talking power (not sure how you feel power I understand physically measuring a force), it is still linear to the area. There is no squared term for the area.
You all passed physics with flying colours but failed your dynamics exam....
Power is a complicated concept for kiteboarding.
Force x speed, simple right?
BUT speed is not windspeed in either the force or the speed aspect of the calculation.
force = (1/2*rho*A*C*Vwindrelative^2)
speed = Vboard (when kite parked)
As someone stated earlier power is not a useful measurement force is what matters
FORCE is what will hurl you into that pile of boulders downwind. and is proportional to the windspeed^2 when stationary. And can be increased based on HOW FAST the kite flies, the speed and angle relative to the wind which you are riding as well as the usable range of angle of attack, All of these will be very different for each kite size so the table is nonsense.
In short it's why a small kite will spank you MUCH harder than a larger one when you mess up. it feels ok when you go out but is capable of generating alot more RELATIVE wind when you accidentally (or intentionally) loop the kite. causing the force to square as a result.....this is when awesome things happen.