That is not the correct template. No where in there does it show the date. If I'm mistaken and that *is* your template, then the date is being added via a plugin.
You need to find the query that grabs all those attachments names/ids/size/etc and add in the ORDER BY statement.
Google "mysql ORDER BY" and you'll get several ORDER BY help pages like this one -
http://www.tizag.com/mysqlTutorial/mysqlorderby.php