You guys haven't obviously tried to upload trailers to Youtube because not all movie companies like their trailers to be shared by random Youtubers or websites... I have had numerous Youtube trailer channels where I have only uploaded trailers, given correct copyright information (not said that I own the copyrights) etc. but still some companies like Lionsgate and Summit Entertainment have reported the trailers and got my channels banned.
Please notice that my channels were not monetizing the views in any way. I didn't put any annotations to the videos nor did I link to any 3rd party websites from the description. Still the companies claimed copyrights to those videos and got them deleted. For example trailers for movies like Machete (I got over 100'000 views in a few days before the trailer was deleted) and Twilight got copyright claims from the companies.
So yeah, I also wonder how that site gets away with hosting the trailers... Maybe they have agreements from the movie companies or something. I would love to know because I have a perfect domain for a movie trailer website but haven't established the site yet because I'd like to get some insight into how these trailer sites work.