That’s just not true. The usual way this is done - after all, a similar thing is already done in other contexts - would be to have a public API run by the state. You can use a hash (generated from say, the serial number of your ID card or passport) to ask certain factual questions. For purposes of this, “Is this person over 18y old?”. The API then replies yes or no.
That’s it. Nobody knows anything else. You could even abstract the serial number if you want to, but we readily give out our names during payment anyways and there’s not much more you can do with the serial. But it could be hashed client-side.
This is incredibly easy to do, to the point where the equivalent part is already done in a whole lot of areas, and in other countries is already used for age-checks albeit not in a game-buying context.