One solution strategy that works very well from my experience is to ask them upfront whether they want to play "for real" or to play to learn. [edit: A third mode is "for (silly) fun" where everything is allowed.] This works for all ages... and for boardgames and physical games. It's their choice which mode they want to play in, and they trust and respect you more when given the choice. You treat them as a peer. You…
How did you get your kids started with board-game type games? I have a 3yro and we just have "silly fun" with dice but I'm trying to figure out how to show him the "move N places forward" mechanic where N is the number on the die.
Maybe start with hopscotch (the regular kind with where you toss an object into a square, but with clearly numbered squares), telling them each time the number of the square they're on, the number of the square they're heading to, and the number of hops they'll do, before they do them. After a while, they'll get an understanding of how the numbers on the squares relate to what you're saying, and maybe even a vague intuition for subtraction.
Eventually, you can replace the thrown object with a rolled die (I suggest a big soccer-ball-sized die they can see from far away, with numbered faces instead of pips)—whose roll indicates how many spaces they should move rather than the space they should move to—and keep playing the same game.
Once they get that, then they're ready to play board games.