The hill is too steep for him. He's making linked hockey stops, not good turns. He's surviving, but has no chance of good skiing. He shows great spirit, now he needs technique.
His feet should be walking width apart. Not spread like that.
Both feet should be alongside each other, not one shoved way out in front.
His outside leg is straight and stiff. There is nothing he can do with it except brace against it.
He's turning everything by swinging his shoulders around in the direction he wants to turn. This is the opposite of a good turn technique. His inside hand & shoulder are dropping down, and it should be moving the other way. The outside hand & shoulder should be lower.
Take him to a run where he is in easy control. Practice skiing with the feet. Feet walking width apart, close to even side-by-side, balance on the balls of his feet. (Good for him, he's not far back on his heels.) Make easy turns by just turning his feet, NOT by swinging his upper body around. Better yet, have him tip his inside ankle to lift the inside ski's inside edge off the snow. Get him to turn his body in the opposite direction that his feet turn. Hands should be in a natural balancing position and about level, maybe with the hand & shoulder on the inside of the turn a bit higher. Have him lift just the tail of his inside ski an inch, no more, off the snow. Let the shovel slide on the snow while the tail is lifted. A good move is to bring his coat zipper tab over the label on his outside ski at the beginning of each turn and keep it there through the turn. He won't get that far, but that's the feeling he needs.
Challenge him on either technique or terrain, never both at the same time. Invent games to make the technique drills fun. One is to carry a glove or hat between his boots without dropping with a reward to whoever, him or you, carries it the farthest. Use your imagination. Safety, fun, skills, in that order for kids (and for all of us). Be sure his boots are a good fit. They need to be as small as possible without discomfort, buckled as tightly as possible without discomfort. New boots every year, of course...thank goodness for ski swaps.