Actually it's an additional security setting available in Safari:
If you want to import/export files from/to your computer under Safari, you should open Safari Preferences, select Security > Website Settings for Internet Plugins > Java and choose Unsafe mode for www.sweethome3d.com web site.

It looks like Apple just wants to kill Java applets technology. Fortunately, they are not #1 and Internet Explorer, Firefox and Chrome didn't go so far!

Thanks to Joshua Smith for his suggestion.