Let’s be careful with definitions. “Internet” usually refers to connections to external services. After initial SONOS setup or when adding a new unit, an Internet connection is not required to play local sources, such as Line-In, TV audio, AirPlay, Bluetooth, or music stored on a local hard drive.
A “LAN” (Local Area Network) is always required, except for Bluetooth feeds to a player. The LAN can be a combination of wired and/or WiFi, as appropriate for the players involved. Controllers and players communicate with each other over the LAN. Bluetooth is unique because an App sends audio directly to a player without using SONOS controllers or the LAN.