It's a bunch of people and organizations around the world offering their software for download over the Internet. It's other people who then possibly pay for and download those apps.
It's distributed, it can optionally include compensation, and how that compensation is delivered is up to the app creator and purchaser.
It may not be as pretty or convenient as what Apple or Google offer, but at least it has the freedom that's desired.
Of course, a package system like dpkg or pkgsrc can be used to help make it far more convenient to find and install software. And websites offering a directory of available software can help with this, too.
All of this already exists. I think that a lot of people have just forgotten about it within the past five or six years.