Why does AWStats show /wp-json* as Viewed URLs

I’m not entirely sure what will be better explanation, or why this one (the real one) is not enough.

In your stats you see URLs of requests and not paths to files. URL has nothing to do with files on server.

Yes – if the requests targets physical file, then that file exists, but… There are plenty URLs that are not connected to any file – mod_rewrite takes care of them. For example there is no directory like /rss/ anywhere in your WP installation directory. There is no directory like /category/uncaregorized/, and yet – both of these URLs work and you can find them in stats…

I don’t see anything wrong in explaining, that your client sees HTTP requests and not file paths. And these /wp-json/* requests are requests to WP REST API.

PS. You don’t see them in Google Analytics, because there is no tracking code in REST API, so there requests are not logged to GA. But AWStats are more like server logs, so all requests get logged.