Nice little detail:
To use the old-style password entry screen on the new Apple TV, wake the Apple TV using the old silver remote, and don’t touch the new Siri remote.
I tested it, and as far as I can tell it works for anywhere input is needed, not just for password entry.
So you get this:
Instead of this:
Personally, I like the new row layout more than the old grid layout, but I know many - a very vocal many - that don't.