Mechanism-first approach. Start from the autopsy finding that anchors the diagnosis: septal thickening. Asymmetrical hypertrophy of the interventricular septum is the structural signature of Hypertrophic Cardiomyopathy. Layer onto this the two clinical anchors - sudden death triggered by exertion and a similarly affected sibling - and the genetics fall into place: this is an autosomal dominant sarcomere disease (commonly $\beta$-myosin heavy chain or myosin-binding protein C mutations).
Why exercise kills in HOCM: the thickened septum narrows the left ventricular outflow tract, and the chaotically arranged (disarrayed) myocyte fibres form a substrate for re-entrant ventricular tachyarrhythmias. Under the catecholamine surge of exercise, contractility rises and outflow obstruction worsens, tipping the heart into ventricular fibrillation - the leading cause of sudden cardiac death in young athletes.
Eliminating the rest: a dilated, baggy heart points to Dilated Cardiomyopathy; a rigid ventricle with prominent atria points to Restrictive Cardiomyopathy; a flabby heart with inflammatory infiltrate points to Viral Myocarditis. None of these produce focal asymmetrical septal hypertrophy in a young patient with a positive family history.
Hence the answer is HOCM (Option C).