Why does alcohol damage the liver and not other organs?

It does damage other. Organs, bigtime. Alcohol damages virtually every human organ system, burns the GI tract, causes bleeding, inflammation, ulcers, burns the pancreas out, kills brain cells, produces major psychiatric problems as well as brain damage, causes anemia, low white counts, serious infections, almost every kind of cancer. Sometimes I think a lot of people have been living in a bubble sometimes :-).
Not just the liver! Alcohol can affect almost every major organ system. It can cause the heart to enlarge, it can significantly affect the nervous system in numerous ways, such as nerve damage, chronic brain damage that may be irreversable, stomach ulcers, vitamin deficiencies. Inflammation of the pancreas, bone marrow damage, increase risk of oral, esophogeal, breast, colon cancer. Abnormal bleeding, to name a few!