This is the API for game plugins, server or client. You could write a plugin that wrote that information to a file (that's what my server status page does) or whatever. It's not the game server's job to handle these sorts of requests really as its better handled externally. The hooks let you catch and write the latest data, though.
This solution is only valid if you host your server and the status page on the same server. If someone register his server on the list, he need to give me access to his file system to be able to know how many players are on his server. That's not imaginable.
My server and status page are on two different servers and I transfer the status page over to the web server as part of the update. It was the easiest way for me to get it working.
So in the future, server owner will have to use such a complicated method just to be able to get something so simple as the number of players connected?
Every game with a server for the past years has a query protocol. I don't really understand the problem you have with that.
Anyone can add this as a mod. However, in general it's the single easiest way to DoS a server, too and a pretty large time sink on my part to get it "right". I have other parts of the game to worry about at the moment.
A server list service could also support a REST API that the server could call to update it with recent info periodically. There are a variety of ways to implement this feature and nothing stops a modder from doing it themselves.
However, the API discussed in this thread is for mods to access. It's part of what a "server status mod" would use to do its job but it is not remotely query-able info on its own. A mod that wanted this support would have to add it... and it's a completely different network connection type than the normal game connection.