Step 1: A chronic drinker with heart failure plus neurological and ocular signs points strongly to thiamine deficiency, the vitamin most easily lost in alcoholism.
Step 2: Thiamine lack produces wet beriberi, where blood vessels dilate widely. The heart compensates with a high-output state, and fluid is retained via aldosterone, giving the edema and raised pressure described.
Step 3: The most severe variant, Shoshin beriberi, adds cyanosis, tachycardia, and engorged neck veins. All of this traces back to one missing vitamin - $B_1$ (thiamine). B3, B6, and B9 deficiencies cause different syndromes.\[\boxed{Vitamin\ B1}\]