No, this solution would work with LAN devices and internal IPs as well, although there would be some extra requirements if it needs to work without internet connectivity¹.
Some things to keep in mind:
* Publicly trusted CAs are not allowed to issue certificates for internal IPs (private network space) or internal hostnames (anything that doesn't end with an ICANN domain).
* .direct is a regular TLD; I'm not aware of anything that would make routers resolve them without internet connectivity. Plex solves this by simply replying to a query for ip.user.plex.direct with "ip".
¹ If you need offline support, or if your DNS cache refuses to accept replies with private IPs (some do, but I think you'd be fine with most SOHO devices), you'll need to manually add those hostnames to your DNS resolver or host file, or alternatively configure your router to resolve hostnames from DHCP leases (many routers do this automatically) and use your "public" DNS label as the device's hostname.