How it’s done
Ask them to teach you their favorite game and play it seriously: learn the controls, die a lot, let them explain.
The stance is everything: you're not there to audit the game, you're there to visit it. When the parent knows the game from the inside, conversations about screen time, in-game purchases, and strangers in the chat stop being abstract sermons and become conversations between two people talking about the same place.
What it builds — the why
Digital judgment built from the inside — the child learns to look critically at their own games because they look at them with you, not against you. Also: few things level the relationship like being the one who doesn't know while they're the one who teaches.
How it changes with age
6–9 Childhood
10–12 Preteens
13–15 Early adolescence
16–18 Adolescence
What to watch for in your child
Notice what your child is after in the game: to compete, to build, to collect, to be with friends? That preference says more about them than the game's title. And if they lose with dignity there but blow up in other places (or the other way around), there's an interesting conversation waiting.