I'm kind of confused about the copyright owner. The provider on Youtube is Warner Bros while the copyright information on the movie saying it's copyrighted by MGM. I searched in the US copyright records but didn't find the record of "Quo Vadis" movie. I just found some records of the music in that movie. I'm not sure if it's still copyrighted and who owns the copyright of the movie.
The discrepancy is due to the fact that although MGM made the original film, Warner Home Video arranged for the film to be re-mastered and restored prior to it coming out on DVD in 2008 (and more recently on BluRay).
Since I assume you don't have access to the original filmstock version, you will need to deal with Warners concerning their digitized version. Given the reported amount of restoration involved I think it is highly probable that a new copyright came into being for the digital version. If this is correct then it will last until 2103, under the US corporate copyright legislation (section 302(c)).