There are a handful of references to the original films ("Get to the chopper!"), but not too many and the directors try hard to make this a monster movie first and foremost. Honestly, the worst part is a convoluted plot device designed to tie in this incident to the Alien/Predator canon right at the end of the film.
spoiler (click to show/hide)
The United States military complex, after successfully nuking a good portion of Colorado - takes technology recovered from the Predator to a "Ms. Yutani" suggesting that the Predator technology was one of the foundations of Weyland-Yutani Industries.
A funny bit of cinema trivia is the Predator the species dispatches to clean up the mess left by the Predator ship crash landing (with the Predator-Alien hybrid on board) was nicknamed "Wolf" after the character with similar job skills in Pulp Fiction (cleaner).