Joe Biden, the former vice president, was four minutes and forty seconds into discussing his new book, Promise Me, Dad, when he got snagged on a memory. We were sitting in the den of his vacation home, in Rehoboth Beach, Delaware. It was a hot day in late summer, and while his wife, Jill, and his sister, Valerie, milled around nearby in casual workout gear, Biden was smartly attired in a checked dress shirt, charcoal trousers, and black tassel loafers worn without socks—as if primed for an afternoon of shirtsleeve campaigning. In his genially raconteur-ish Uncle Joe way, he recalled how eye-opening it was, 25 years ago, to read Richard Ben Cramer’s What It Takes, a chronicle of the 1988 presidential election that is considered a modern classic of political…