The point is creating a new network identity that is not connected to your public identity, and let Google etc track it all they want. So it's pseudonymous more than anonymous.
You mustn't use your "onymous" Google ID on this burner phone, nor have any contact between your pseudonymous Google ID and your public Google ID. I guess the guide should spell this out more, I took it as implied when the guide started by buying a non-trackable phone with cash.
Edit: quote from the guide: "11. Only use this device for Signal (and maybe Google Authenticator, see #13) from now on to minimize its exposure."
It's even worse - simply using the same wifi point as your other Google accounts or even your friends will deanonymize you.
Trustable local software (so not GApps/Android) and a mix network is the only way to get anonymity.
I'd personally like to see communication apps that use TOR for messaging, with the option to explicitly break anonymity for voice calls - leaving your location untracked most of the time.
