The aerodynamic force involved is called lift. Lift on a kite is perpendicular to the relative wind direction. It is the actual wind, the actual direction of wind and speed of the wind. The kite reacts to the wind pushing on it. Lift is exerted in an upward direction thereby opposing the pull of gravity on the kite.
Air is made of particles that are in constant motion and air is actually quite heavy.
A cubic yard of air will weigh 2 pounds at sea level. Air will resist motion of any object through it. You can test this by trying to move forward while holding a flat surface in front of you. The speed at which you move is resisted by the air on the flat surface. A kite is sort of an air deflector.