This is gonna be a big spoiler. Let the reader beware.
Spoiler for NervGear moving to hospitals:
At some point after Episode 1 takes place, everyone was struck unconscious/asleep for about 2 hours, which was the safe time Kayaba gave to the govt to move the SAO victims to hospitals. In-universe, it was suspected that the NervGears were placed into sleep mode. After that, they were stuck for good.
Also, the next gen VRMMO headset, the AmuSphere, is wireless, as is the NervGear - note the WAN light and the power button. My guess is that it's either a power cable, or an interface for installing from PC to NervGear, like how you can pop a disc into a PC and set a specific hard drive for your game installs.
Or Kirito's house already has wired ethernet ports - in my old house we actually wired up a few places with ethernet cables, before switching to wi-fi in our current place.