The Chernobyl nuclear disaster convinced Gorbachev to make the decisions that led to the end of the cold war. George Bush#1 presumably benefited from good feelings people had about the Reagan years, which may have been due in part to the end of the cold war in 1987*. If the cold war had still been going on at the time of the 1988 election, would Dukakis have won?
*Many historians would probably say that the cold war ended with the fall of the Berlin Wall in 1989. I maintain it ended in 1987, the year Reagan and Gorbachev signed the INF Treaty.