MSFT needs to do a better job of specifying what product their help docs refer to. That video shows the next version of 365 which is currently only in Preview, Yet it states:
Applies to:
Office 365 Small Business admin, SharePoint Online Enterprise (E1 & E2), SharePoint Online Enterprise (E3 & E4), SharePoint Online Midsized Business, SharePoint Online Small Business, SharePoint Online Website
Which isn't true at all. How hard would it be to add "only applies to 365 Preview version" in the title? I'd fire myself I made an obvious mistake like that!!
Take a look at "customizing your O365 public site" on this page. Choose it from the drop down.
In the current version:
You can edit html in Sharepoint Designer (but not the master page)
You can change navigation
The admin settings available are accessible via domain.com/_layouts/settings.aspx
The gadgets are the only web parts you can use.