While it all sounded very cute with a little kid speaking on the frequency this is surely going to end up with the controller being fired. I have had loads of people over the years plugged in with me and watching what i do. Friends, family, pilots, work experience kids from school etc, at no point have i thought it would be a good idea to let them have a go on the frequency, even with my strict supervision. I think from a UK (Nats) perspective this would come under the umbrella of gross misconduct and you would be shown the door.
I'm sure dad had junior on a very tight leash but what if an incident had occured that had nothing to do with the controller, like a runway incursion. Or what if dad, god forbid, made a mistake, and junior clears someone for takeoff with traffic on the runway. 75 people died when the aeroflot pilot let his kids 'have a go' a few years back. That was under strict supervision as well, and I'm sure dad in that case was a good pilot and a nice guy just showing his kids what he did for a living.
I'm sure the JFK controller is a nice guy but his actions here seem to be poor judgement at best. I hope he gets away with a warning but i fear the worst for his career.