Why does screentime's "Only Approved Websites" limit the functionality of the approved web address?

Autism wrote:

For example, a website like miniplay.com functions perfectly before turning on screentime.

Once it is added to the "Only Approved Websites" the web address works but all the game screens are black.

But, if the website is under Limit Adult Websites and added to the Always Allow section, it functions fine.

What exactly is the "Only Approved Websites" feature blocking so that the website does not function at 100% even when it is approved? (ipad)

Probably because content on that web site is being pulled from sites that are not on the approved websites list.

Possibly. You would have to add every domain that the page is pulling content from.