You stated in your post that you are both in your 60s, correct?
In 2016, you will be 5 years older than you are now.
Do you want to look back on those years as a time you spent chasing after a man who is hooked on his ex, enslaved to his addictions, emotionally distant and just an all-around ass?
Or would you rather look back on those years as a time you learned about yourself, picked up a new hobby, traveled someplace new, enjoyed your serenity and got well and whole?
I don't think the former is how you want to spend your future. If you truly believe in "enjoy it while you can" then spend it in the best way you know how. Chasing after an alcoholic isn't it.
You probably don't deserve to be dumped. Many people don't. But this is probably a blessing in disguise. IMHO, you are better off alone and hopeful than paired up and totally miserable.
Let him go. He already has a girlfriend and her name is Alcohol.