How did Eli die when he heard the ark had been captured?

Answer: He fell and broke his neck

When the ark was mentioned, Eli fell backward from his chair by the gate. Being old and heavy, he broke his neck and died.

“As soon as the ark of God was mentioned, Eli fell backward from his chair by the city gate, and being old and heavy, he broke his neck and died. And Eli had judged Israel forty years.”— 1 Samuel 4:18 (BSB)