When I test this out I can get the option to edit the menu, but not for editing the contents or the theme. It seems that there have been edits made to the code on the template page and the menu's contents are no longer editable on the page.
You could just choose to edit the menu, then make your updates to the preset and apply the newly updated menu to the page. Do you have the option to edit just the menu from the Property Inspector? It should be available to you if you have the invisible scripts enabled from the preferences and in the visual aids. You will need to select the shield icon for the menu, when I view your page I can see that the icon is partially hidden behind the tab for the main content. You can also select the js code on the page to get the edit option. Here is the code on the page you would need to select:
It is on line 194 in the page you sent me.