When the client says that it is not connected directly to the server (but the server is in the same local network), it usually means you have either a general issue with DNS or with “DNS rebinding protection” specifically.
First step: try using the hosted web app in a fresh web browser session: https://app.plex.tv
Disable any web browser add-ins you might have activated. If that clears the error, re-enable them one by one and repeate the playback test until you have found the culprit.
Second step:
configure your router or your computer to use the DNS servers of Google: 8.8.8.8 and/or 8.8.4.4
Third step:
look for configuration options in your router/DNS resolver about DNS rebinding protection and create an exception rule for the domain plex.direct: https://support.plex.tv/articles/206225077-how-to-use-secure-server-connections#toc-4
