Does having cirrhosis mean the person is an alcoholic?

No. Alcohol is only one of many causes of cirrhosis. Other comon causes include viral infections (e.g. Hepatitis c), autoimmune disorders (e.g. Autoimmune hepatitis, primary sclerosing cholangitis, primary biliary cirrhosis), metabolic abnormalities (e.g. "fatty liver" disease, abnormal copper or iron storage), and certain medications.
No. The number one cause of cirrhosis in the world is hepatitis b, mostly in under-developed countries where it is widespread (africa, south america, south asia). In the us, alcohol used to be the number one cause of cirrhosis, but it has moved to second place to hepatitis c, which is mostly spread by IV drug use and used to be by blood transfusions. The combo of alcohol/hep c makes cirrhosis worse.