In the movie Twister 1996 these two movies (The Shining and Psycho ) were played at the drive-in so as to signify the collaboration between the Universal Studios and Warner Brothers.
The project was a co-production between Universal and Warner Bros.
That is why the drive-in marquee shows Psycho (1960) a Universal
release and The Shining (1980), a Warner Bros. release.
Source : IMDB Trivia section for this film
Twister was produced by Steven Spielberg's Amblin Entertainment, with
financial backing from Warner Bros. and Universal Pictures. In return,
Warner Bros. was given the North American distribution rights while
Universal's joint venture distribution company UIP got the
international distribution.The original concept and 10-page
tornado-chaser story were presented to Amblin Entertainment in 1992 by
screenwriter Jeffrey Hilton. Steven Spielberg then presented the
concept to writer Michael Crichton. Crichton and his wife, Anne-Marie
Martin, were paid a reported $2.5 million to write the screenplay.
As to another anticipated reason for this, apart from the obvious is:
Also during the shining movie part a very violent tornado comes,
everyone goes into an underground sort of area, and the roof is ripped
off, which is just like what happens in her childhood as well. And
while this is happening we see the movie sign, which says, The
Shining: And below it "A Night of Horrors." Which is what the
characters are experiencing as well. They showed the movie instead of
being torn apart in the tornado at the end, dissolving, as Jack and
Wendy are talking back and forth. Which seemed ghostly again to me. Or
to be meaning something.