“The site owner” is Warner Brothers, they likely have a department responsible to keep movie-related websites up - and might well do it in-house, after the AOL acquisition. A site like this is basically free to host: a domain registration for 20 or 30 years will attract a massive discount, space on disk is probably less than 50MB, used bandwidth is minuscule... after you set up log rotation by file size and automated domain renewal, you can basically forget it exists.
Its quite possibly literally just a bunch of static html files. There is not much maintenance cost there. They probably run all their static sites from the same webservers. It may very well be the same effort to keep it as to delete it.
It's running on a fairly current version of Apache, but aside from keeping the server up to date, it conceivably could be running the same setup for years.
For an organization the size of Warner Bros, it's essentially free, as they are literally doing nothing to the server for that site specifically.
However, it does look like it's running on AWS using their global accelerator (globally optimized traffic) so I assume it's sufficiently robust.
I would guess because of the trademark: keeping a bunch of static HTML files around is not much cost otherwise, and certainly gathers some attention like this post on HN indicates.
Obviously the site owner is intionally keeping the site up and dealing with outages.
But I wonder why?