Just to give an update on the situation.
I submitted a DMCA request here. As yet (5 days later) it has not been responded to but the offending domain has been offline for 3-4 days. Not sure who took it offline.
Still Google is ranking the offending domain instead of mine. In fact if you search for my exact URL (http://www.naturallivingideas.com/drinking-apple-cider-vinegar-benefits/) in Google, it still brings up the offending domain.
How long does it take for a site to be removed from the index once it goes offline?
James