No, he very much was not holding the rifle correctly. Lets pretend we're liberals and take this tip to butt. To kick things off, his left hand needs to be grabbing the stock in order to pull the rifle back into himself. Also, his elbow should be down instead of out in order to minimize his profile. As for his right hand, he's violating the second rule of firearms: Never touch the trigger. Also, the buttstock is way to high; It should be down, about an inch under his collarbone. Lastly, he should be squared off against the rifle instead tucking his torso along-side it.
He has obviously never fired a weapon in his life. I bet he'd be easy to bully.