It's mentioned explicitely in the first message sent by slack (rejecting the listing of the app). First paragraph of the article.

AFAIK Github apps work the same way. Additionally, you need to meet a specific number of customers (I think over 200) to apply to be listed in their market.

Exactly correct. In theory, GitHub's app marketplace offers developers a separate option for "unverified listings", which have "no minimum install or user count requirements", but requires your app to be free.

However, when I submitted a new app as an unverified listing last year, I received a rejection email stating they were only "looking for apps with at least 25 installs". I attempted to appeal (based on their marketplace system's text directly stating there was no minimum user count), but I received no response, and none of the ~dozen engineers I personally know at GitHub were able to help.

I can still make my app available, and implement a third-party billing system, but without a marketplace listing it's much harder to gain exposure and users.

All in all, developing a GitHub app was an extremely frustrating experience, especially since GitHub extensively makes internal use of my open source project upon which my GitHub app was based.

That's correct, it doesn't prevent distribution. Also, I believe Slack will show a warning on your app at install time if it is not listed.