I think it would be a good idea to have ESRB ratings on the games in the overview so parents can make smarter decisions on which games their kids should play. A parental permission code or something to keep kids from playing more mature games would be a convienent feature are well.

the problem is that some of the games predate the esrb, and that games on digital distribution platforms don't need esrb ratings to be sold.

And, with the games being DRM-free there is no way to actually lock kids out of playing games above a certain raiting like the OP requests.
Even if that feature was added to Galaxy, the kid could easily run the game directly from the exe.

Here is how my friends do it: The parents keep the password to the GOG account and they buy new games together with the child(ren), then download and move the games to their computers/OS accounts.

I for one think locking my parents out of the computer would be a great idea.

That assumes that the kid actually knows how to do that...

Chances are thery are way more likely to know how to than the parents

Right, but some kids will know that and then GOG will get complaints. The only way it can be reasonably secure is with DRM.

Incidentally, I definitely would have known how to run the game from the exe as a kid. My parents first computer was a windows 95 pentium MMX in around... 1996/7 I think? Anyway, I knew every nook and cranny of that thing.

If we were talking about mobile devices, I'd wholeheartedly agree with you, as my, not so obvious apparently, point was that kids today are more savvy with knowing/doing all sorts of things on mobile devices than things on PCs that are not of the "one button" variety. At least that's my observation. We're talking about very different generations here, see above.

I think the OP has in mind something like the parental code for TV works? That could perhaps be implemented as a filtering option in each account, so when it's enabled titles with gore, violence, etc. are excluded when browsing the catalogue, and disabling it would require to enter one's password, or one of those account verification codes? That's assuming that kids use their parents account, and not their own where they have 100% control over account settings.

I'm not sure I get why the OP requests the ESRB rating system specifically. Don't the ratings systems in use give enough information on whether they're suitable for kids or not?

I was thinking more of a authentification code lockout on the play button. that to me seems like the most direct way to
lock out a child from playing a game to violent for them. Obviously if the child is very good with computers they can get around anything, but, I would imagine that percentage of kids is low. It's more of a convience thing for the parent so that they may prevent their kid from playing something they don't want them to. As for the ratings, it's an idea that reviewers could fix with their comments. Put a few age brackets to pick from or choice descriptors that parents can breeze over to see what sort of content a game has in it without having to buy it. I think anyone who reviews a game can tell people what to expect. That could be a rating system.

Many game entries have the PEGI rating on the GOG store pages, which has jurisdiction in Europe where GOG's HQ is located.

Sites like MobyGames have listings for these games and more across multiple rating systems, including ESRB. So all it takes is a few search forms.

Mobile phonos, jocko homos !

Because he's from the US and doesn't know what PEGI is. Not all are as enlightened as we are.

Regardless of whether they know what PEGI is (it's a simple look up if one doesn't), isn't it clear when the game page says: or that said game isn't suitable for children?