Although often thought of as a parody of Jurassic Park (1993), the plot actually has more in common with the 1973 film Westworld (1973). Both of those films, however, are based on stories by the same author, Michael Crichton.
The reference at T.G.I. McScratchy's, where it's always New Year's Eve, is a reference to Walt Disney World's Pleasure Island. Starting in 1990 and running through 2005, Pleasure Island celebrated New Year every evening.