The router has (at least) two interfaces. Your
nmap 192.168.1.1 scans against the internal interface and lists the services the router is providing for your LAN (DNS, web interface for administration etc.). That's a different set of services than the services it's providing for the wild Internet on the WAN interface. Scan from the Internet should only list the services you have planned to expose; possibly none on a home gateway.
You can log into your router (
http://192.168.1.1) and browse the web admin interface to disable all the services you don't need. E.g. if you don't use HP JetDirect, it's a good practice to disable it even if there's no current vulnerabilities involved. On the other hand, Universal Plug and Play (UPnP) can be used to open inbound ports, exposing your LAN devices to the Internet, and can be consider as a threat.
Port by port with a little help from NETGEAR R6400v2 User Manual. (Usually I wouldn't dig this deep for a single product I don't own, but the arrogant attitude on the NETGEAR Community made me.)
53/tcp (domain). There's no option to turn DNS service of, and it is required as the DHCP server on the router always introduces itself as the resolver.
80/tcp (http). Used for network administration and can't be closed.
- Also used for file sharing from USB drive and enabled by default; I'd recommend disabling it (from ADVANCED > USB Functions > ReadySHARE Storage).
548/tcp (afp). Apple Filing Protocol is related to file sharing; disabling ReadySHARE might affect.
631/tcp (ipp). Mac OS X Printer Sharing. (Same explanation as for
5000/tcp (upnp). Like explained, this should be disabled (ADVANCED > Advanced Setup > UPnP).
8200/tcp (trivnet1). This isn't Trivnet. It's MiniDLNA Media Derver (Chapter 8, p. 94).
9100-9103/tcp (jetdirect). NetGear calls this ReadySHARE Printer Utility (Chapter 9). It's controlled with an external utility. Not sure if could be disabled.