The movie Donnie Darko is timed in the 80s (to be precise 1988), but the movie was released 2001. I can see no significance, to put it in the past. Yes, there was the presidential election, but that is only background for the plot in Donnie Darko. The same plot would have been possible to place in 2001.
I think this was done as a way for Kelly to show a more simplistic time rather than a time with all the technological advances being made. Also, there is a theory I saw here, in fact about the way the number 88 is a theme in the movie which would explain a lot about using this time period.