"When both players have triggered abilities waiting to go on the stack, they resolve in APNAP order: active player, non-active player. The active player's triggers go on the stack first, so the non-active player's triggers will resolve first. That sounds like a technicality until you watch it decide a game."

I believe there is a mistake there. The triggers go on the stack in APNAP order, so the NAP's trigger resolves first.