This is evident from the following details:
* The animation style: The animation style of the film shown in the movie closely matches that of Disney's classic 1959 "Sleeping Beauty."
* The "Sleeping Beauty" song: The children in the movie sing a line from the iconic "Sleeping Beauty" song, "Once Upon a Dream," which is specifically from the 1959 film.
Therefore, the version of "Sleeping Beauty" they are watching is indeed the classic Disney animated film from 1959.