fgsfdsfgs has released a port of Quake 3 for the Nintendo Switch:
Installation
Extract ioquake3nx_v010.zip onto the root of your SD card.
Copy the baseq3 folder from your Quake 3 installation to /switch/ioquake3/. DO NOT replace any files if prompted. Make sure the baseq3 folder contains files pak0.pk3 through pak8.pk3, i.e. you have installed the 1.32 Point Release patch onto your Quake 3 installation.
Run ioquake3-nx from Homebrew Launcher. The NSP version of hbmenu is recommended, as some actions require additional memory (e.g. connecting to almost any online server).
WARNING: This port is still very glitchy. Expect crashes and below average performance.
If it crashes, check /switch/ioquake3/crashlog.txt for information.