I am not a big fan of semi autos for very young shooters. While it does supply the instant gratification, that has become too ingrained in our culture, it does not encourage building marksmanship skills.
You mention video games, a bane of modern parenthood, and I agree that kids these days NEED to be PULLED away from them. I will not belabor that point. Your son is lucky his dad is actually interested in being a dad.
Here is what I would think about getting for him
Henry Repeating Arms | Fine Rifles Made in America and Priced Right
Cool enough to perk his interest, works well for a lefty and not prone to developing the spray fire mindset.
RAL