The DMG file uses Apple Java 6 not Oracle Java. Nevertheless it's a strange error and the program doesn't seem to have been launched correctly.
But, as you already installed Oracle Java, please try with the Java Web Start version: download http://www.sweethome3d.com/SweetHome3D.jnlp file, double click on it (if the system refuses, click on the SweetHome3D.jnlp file while keeping the ctrl key pressed and choose Open with > Java Web Start).