I just bought a new ring chimes. I followed the instructions and it came right up and started working. I was not asked for my LAN password at any time. I’m pretty sure that my router would not accept a new wireless LAN device without the right password So how did the chime device get the LAN password?
Because you had at least one other Ring device and the Ring app.
When you connected to the chime, the app asked ‘Connect to your network?’ (which you had used previously for existing items) and you replied ‘Yes’.