If not for that ad, Bush would have become President. In fact anything could have changed the outcome: not picking Dan Quayle, no 1987 stock market crash, no Iran-Contra, etc. The only reason that election was so close was because of Cuomo's liberalism and rumors of his mafia ties. Bush's campaign manager, Lee Atwater, helped develop a smear campaign against Cuomo's Italian-American background.
I think you mean in OTL the incumbent Democratic Party held the White House until 2000, right? Cuomo was re-elected over Bob Dole in 1992. Vice-President Lloyd Bentsen declined to run in 1996, the same year that the Gore/Kerry ticket narrowly defeated the Republican ticket of George W. Bush and John Danforth. Only in 2000 was the Democratic hold on the White House broken by John McCain.