Well there are two Online Accounts Apps in Ubuntu:
gnome-contacts App is a Gnome Application and therefore uses the Gnome Online Accounts App. But you use the Ubuntu Online Accounts, which curiously do not link the Address book of the Google Account.
Install the Gnome Online Accounts in Unity
Install Gnome Online Accounts with:
sudo apt-get install gnome-online-accounts
After that you must activate the Gnome Online Accounts for the Unity Desktop [Source]:
Change in the file:
sudo nano /usr/share/applications/gnome-online-accounts-panel.desktop
the line from
After that you should see two Online Accounts in System Settings and in Unity Dash. Add your Google account also to the Gnome Online Accounts and you should be able to see your Google Contacts in the
gnome-contacts App (perhaps you must change your Address Book in the menu of
gnome-contacts with change address-book to the google address-book of you choose local address-book before).