Place the NRO into /switch/nxquake/ on your SD card.
If you only have the shareware version of Quake, copy pak0.pak to /switch/nxquake/id1/. If you have the full version, copy both pak0.pak and pak1.pak to /switch/nxquake/id1/.
If you want to play Scourge of Armagon, copy pak0.pak from hipnotic to /switch/nxquake/hipnotic/. If you want to play Dissolution of Eternity, copy pak0.pak from rogue to /switch/nxquake/rogue/.
Make sure the pak files and the id1 directory have all-lowercase names, just in case.
You can run NXQuake using Homebrew Launcher.
If it crashes, look for console.log and error.log in /switch/nxquake/.
Mission Packs and mods are supported. If you have more game folders than just id1 in /switch/nxquake/, a mod select menu will pop up when you launch NXQuake.