I started shooting at 5 using a good ol 22 Chipmunk rifle (cricket uses a cheap copy of their design). Within the year I was fireing handguns again all .22s. By time I was your sons age I was shooting my fathers Mini 14 and AR which is now mine. I think that same year I basically started shooting everything in the gun cabinet I wanted except the BAR in 300 Win Mag and the custom Weatherby that had been my grandfathers. Safety was always the number one rule when we went shooting and when I handled guns at any point.
When we would get home from the range I was responsible for checking all guns and stripping them down and cleanining them. That also gave me a better respect for them as a tool and gave me an understanding as to how they operated.
By time I was 15 I built my first custom fire arm and these days if someone in the family, or my fiances family, needs any work done on their guns I am the one they bring them to. In fact I was just brought a Savage 110 in 270 that you could not hit the broad side of a barn with. Sadly I discovered the barrel was badly bent off to the right side. Looks like I will soon be rebuilding my first Savage, he wants me to turn it into a precision rifle and I may change the caliber.
Anyway back on track yyou seem to be doing well by your son when it comes to firearm safety and responsibility. I still have photos of my early shooting trips with my father and those are cherished memories. I would also agree with others that CoD more than likely would do more making a kid want to shoot something "terrorist style" than proper instruction at the range. I however would have also included in the video you giving him safety instruction and going over the operation just to show that part of things.