How do you play on Wolf Quest multiplayer without an account?

You cannot.

Registered accounts are required to utilise WolfQuest Multiplayer. This way, any cyber bullying can be dealt with, as can any rule-breaking. Registering an account is free and easy, and account activation occurs within a few days of registering. ^^

Link provided below in the sources / related links for you. With a registered account, you can use the WolfQuest forum to participate in discussions around the community and more.