"Local" meaning on the same machine as the MC Server, with all other machines being clients. That's how many of us run it. Having the DB on the NAS with multiple MC instances using it is asking for trouble, as PC1 can change the DB without PC2 seeing it, and then PC2 can overwrite the changes. There should only be 1 MC server managing the DB files; all other machines should connect to that MC instance as clients without direct access to the DB files.
You're asking for a QNAP/Synology MC server version (which I think existed as some point), and Jim is pointing out that a QNAP is really just a non-standard linux machine. There is a Linux version of MC and you can have any generic low cost PC running linux and acting as an MC server, with the DB local to it (for performance), backups to the NAS if you wish. Even a Raspberry PI works, or a low-power NUC. Just not a QNAP or similar due to the non-standard Linux OS.