Alcoholism is a sin. Just like any other sin, it holds us in bondage, and we cannot escape.
Only the power of the Holy Spirit can break the bondage of sin, and that will only happen when we have faith in Jesus Christ, and his sacrificial, atoning death for us on the cross.
This applies to every person, and sin of any description.
John 8:36
If the Son therefore shall make you free, ye shall be free indeed.
In your scenario it is still a personal decision that one makes. It is not forced upon them, each individual makes a free choice to ask for help. I choose to think that God granted us the tools to control our bodies and minds if we choose to utilize them, just like he gave us the power to recognize good and evil. Forgiveness for one's actions is another topic entirely.
It is a failing of the human character. Do you call people who are in Overeaters Anonymous sinners?
"Alcoholism is a sin."
Perhaps it is. But please remember, being a SOBER ALCOHOLIC isn't a crime or a sin. Some people have difficulty getting that straight.