The cause for this is the header that is being sent in freemind_export.php line 52.
Because the file is downloaded as filename.mm.txt, you cannot directly open it in freemind. We have to get rid of the txt extension triggered by the header.

If you replace this header with the following:
header( 'Content-Type: application/octet-stream; name=' . urlencode( $t_filename ) );
everything will work just fine, the file is save as .mm and you can also immediately open it in freemind.