Well, here's the thing. From what I can find, the absolute cheapest Z370 motherboard on Amazon and Newegg (required for a Core i3-8100, unless those run on 200-series boards) is the $110 MSI Z370 Pro-A. To accommodate that board, we also have to switch out the case for an ATX case and spend more that way, too.
The board I picked out in the OP is more than $30 less than that. So if we're spending around $35 extra on the CPU and around $35 extra on the motherboard and have to pop an extra $10 or so on a case, suddenly we save zero by going Intel with integrated graphics vs the Ryzen 3 and RX550 combo. And I think the AMD setup is probably going to perform better in situations where you'd actually feel it, which is the limited selection of games available to the kid.
We are going to spend a few bucks extra on RAM, but I think this is otherwise pretty much set. I did find a $110 RX460 4GB (which should perform roughly equal to the 560) and the dad is mulling it over, but we might get that instead. Next is to wait for Black Friday to ruin all of our plans.
I do not understand what I do. For what I want to do I do not do, but what I hate I do.