Well, now, y'all are forgetting one thing.
He didn't say *which* Kennedy was Dole's oppoent.
So...
1963: JFk elects to skip Dallas after suddenly suffering severe back trauma from a fall. Though mildly better as '64 dawns, he is incapacitated enough, as his Addison's Disease progresses, that he chooses not to run in '64. (He also suffered from serious back pain, from what I'd heard.)
1964: Lyndon Johnson wins election, in something of a sympathy vote. Civil Rights legislation passes, as some consider this a Kennedy legacy.
Without the strain from the Presidency, JFK's Addison's Disease isn't quite as bad. When LBJ gets less and less popular, JFK is urged to run again.
1968: JFK wins re-election, the 2nd man to ever win 2 non-secutive terms. Despite his popularity, he refuses to support an amendment that would change the Constitution to only forbid more than 2 consecutive terms.
1972: Richard Nixon is elected; his trips to China and the USSR in his first year, combined with successfully keeping the Yom Kppur War from becoming a World War III, give him great support, meaning as he pulls U.S. forces out of Vietnam in 1975, he is considered a hero enough that he doesn't try to pull any dirty tricks such as Watergate. Harold Stassen is in the Nixon cabinet in the late 1970s, where he proves himself worthy as a leader in a few areas.
1973: Arab oil embargo does make economy weak; whie Nixon isn't as impacted by it in his first term, by his 2nd the economy is the main issue.
1976: Robert Kennedy runs for the White House, but loses to the incumbant Nixon. However, he makes a very strong showing.
1980: Trying to impress someone, John Hinckley fatally shoots Ronald Reagan, the probable Republican front-runner. He had considered President Nixon, but never got the chance, and felt the Republican front-runner would be the best bet instead. George H.W. Bush thus becomes the Republican nominee.
1980: On the Democratic side, Robert Kennedy tries for the Democratic nomination, but is in a close battle with Jimmy Carter before being shot by Sirhan Sirhan. However, because of the assassination of Reagan earlier, there is enough security Kennedy is only badly wounded. Instead, Carter wins the nomination, and the Presidency. RFK will be in a wheelchair the rest of his life.
1984: Robert Dole defeats Jimmy Carter and Walter Mondale, as Carter is seen as weak on foreign policy, and Dole reminds some of the strong Republican foreign policy of the Nixon White House.
1988: Now sufficiently recovered, Robert Kennedy would like to make another try at the White House. However, Dole is incredibly popular, and it's doubtful he could win; relations with the USSR have cooled considerably, and Dole is getting some credit for winning the Cold War.
Democratic Party officials decide to let RFK try, anyway, as they worry that people will remember FJK's incapacity and worry that RJK will suffer the same fate. Therefore, he is nominated, and loses by a fairly large margin, tho it's not an electoral blowout.
1988: Meanwhile, Robert Dole's VP dies in office in early 1988. (Candidates?) Dole, feeling sorry for Harold Stassen, names him VP, figuring he will nominate someone else at the convention in a few months. However, a large outpouring of support, and the fact that the Democrats have nominated a man who isn't as likely to win, makes him keep Satassen.
(Note: if you wanted *Ted* Kennedy, then you could probably have RFK assassinate in 1976, Scoop Jackson run, then Carter in '80, and Ted Kennedy in '88. Wonder what the latest is you could put JFK in there? He'd have only been 71.)