We agree that motion would be similar to releasing a ball that you are spinning in a circle by rope. When released, it continues with the instantaneous tangential velocity at that moment. However, the skateboarder's center of mass (lower torso) is somewhere on the order of 2.5 to 3 feet away from the ramp surface. Fundamentally his circular path of motion is offset from the ramp surface. Over course of his free motion from release to re-contact, he's only in the air long enough for his center of mass to get closer to the wall by like 3ish inches. Therefore, he can clear the ladder and quickly get back to the board before hitting the ramp wall.

He would go straight into the wall if he continued in his path for a significant part of the curve. This is obviously an approximation, but he's only in free motion for like 3-5 degrees of a circular arc. That's not a lot in the grand scheme of things. After which, his feet are back on the board and he receives the necessary centrifugal force again to get back in the path of the arc.

Edit: Keep in mind that he keeps his current velocity vector when his feet leave the board. The absence of his feet on the board doesn't mean he suddenly gets sucked into the wall (where would that force come from?)

Late to this is post, but look carefully at his legs. He's not "jumping", he merely retracting his legs toward his body and it gives the illusion of jumping. As someone else pointed out, momentum does the rest.