An official forum posting by "Gary A." from ZeniMax Online Studios said that those who purchase The Elder Scrolls Online on home consoles will need to redeem a key in order to play the game. Yes, the console version of the game has a key redemption tied to it just like the PC version of the game. And yes, this also means that you cannot trade the game away after that key is redeemed.
To clarify, you will need a unique game registration code in order to play the game, and used copies will not be eligible to receive a key if the code has already been redeemed.

It works the same way as the PC version in that the code included in the box is to activate your ESOTU account and the discs are for installation purposes. If you own the disc but don't have a key, you'll be able to install the game and reach the login screen, but you won't be able to log in and access the game without an active ESOTU account.

It's not very clear right now how this will affect those who share games across multiple accounts on the same console. It's also not very clear if ZeniMax has a solution in place for those that acquire the physical disc secondhand and wish to buy a new key or account.