Assuming approval is a strict requirement, a middle ground solution would be an open source, federatable, steam clone, operated locally. Have an approving committee to priorise approving games from local developers, and working on evaluating international games after all local games are dealt with.
That's for sure similarly efficient to gaming industry distributors system, where you need companies with the right connections to launch games in big platforms, like sony's, nintendo's, or microsoft's. Or event steam's, to a minor extent. Which also veto games not aligned to their opaque terms and conditions.
Also, it would improve international competition, with the removal of the technology barrier of entry, distribution costs would lower, games would become cheaper, and the share retained by creators and developers would be increased.
Long live, a collaborative approach to technology! Long live smaller profit margins! Long live open source!
How do you even stop distribution of malware though? For a second or two I thought this would be a really cool idea to start working on; but assuming everyone can spin up their own instance there's nothing that would stop someone with evil intentions to create a fake store that federates with all good storefronts.
I was thinking federation for the social aspect of it, not the distribution aspect of it.
Distribution would be "the usual". Stores acquire software, and licenses, store and serve the data through a server. Client software solve installation and integration between games and social stuff, like friends, messages, networking and achievements.
I mean, it's not a one person project, but if I were supreme leader of Vietnam and had the people and resources to be working on providing video game entertainment for the masses, that's how I'd be thinking about it. Not that software skills and supreme leader skills have any overlap...