Templafy integrates with SharePoint 2013 Online and SharePoint Online for Office 365.
Company templates can be accessed via SharePoint online and opened directly in MS Word online.
In SharePoint online
Navigate to your team site and go to "documents". Here you'll see a "Create document button" with a Templafy icon on.
When clicking "create new document" you are shown the same view as if you accessed Templafy Web, but this is technically still within SharePoint.
The document is saved in the document library from where the document was created.