The easiest way to see if the plugin is installed is to check for the Tabzilla preference page in your Notes Preferences.
Open the Notes Preferences dialog by choosing the menu option File – Preferences. You should see an option on the left for "panagenda Tabzilla":
If this preference page doesn't exist, you don't have the plugin installed. If the plugin is installed, you can see the version of the plugin at the bottom of the preference page.
It's possible that your preferences have been changed to hide all the menu items. Open the plugin preferences page as described above, and make sure there is a checkmark next to all the items in the "Activate these menu actions" section. Then click OK and try right-clicking an open tab again.
By default, the Tabzilla plugin will not close your Home, Discover, Workspace, or Mail tabs. You can change this by opening the plugin preferences page as described above, and checking or unchecking items in the "Allow these tabs to be closed by a menu action" section.
Also, the Tabzilla plugin will always leave at least one tab open, to ensure proper functioning of the Notes client.