Thanks to
RaymondRis for this great blog post –
http://blogs.technet.com/b/raymond_ris/archive/2013/04/04/cannot-open-or-create-word-documents-in-sharepoint-2013-with-office-2010-and-project-2013.aspx
explaining how, after loading Project
2013 this can make your SharePoint libraries default to the 2013 versions of
the protocol handlers.
The fix is
easy – go take a look at Ray’s blog.