I'm often the guy learning and explaining the rules in my group. The guys toss me the names of the games they have bought and I go to youtube to find a video like this: Terra Mystica.

Maybe those videos don't cover everything, but you can fill holes by checking the actual rules book later. I don't think an MtG player has any right to be intimidated by a board game's complexity

I will bring up Puerto Rico with these guys, one of them probably has it.

@Cucho:
For your 7yo Catan is a safe choice imo, all the other games are for grown-ups - and some of them stupidly expensive. Catan is a totally valid game for that age, maybe even a bit much.

Also when factoring in kids, RNG can actually be a positive thing - because it spreads wins more evenly over differently capable people.

Another game that comes to my mind for the purpose of playing with a kid is Wingspan. That's a recent game about birds - quite interesting actually, because it has many species with accurate descriptions as cards. I've played it twice and it is certainly more of a family game than an actual competitive one for adults. But since you're looking for just that, I can recommend it. Check out a few minutes of the video.