No, they're not part of the StackExchange Network in any way.
This website called NameThatMovie (http://namethatmovie.org/) looks very similar to a StackExchange network site.
Their design and structure was simply partly inspired by StackExchange to some degree. Yet they lack many features therefrom, first and foremost the whole concept of votes and reputation.
I found the website's poster on the right sidebar on movies.stackexchange, the website is primarily a Q&A site for identifying a movie. But there is no mention of it being a SE site anywhere on the site.
That link on the side bar is just an advertisement for this site, seeing that it is related to the topic of movies and might be a good place for people looking for identification to find their answers. The Community Promotion Ads are created and voted for by the community for stuff that might interest them. But those ads don't need to have anything to do with StackExchange at all.
Maybe I misunderstood something, was it just an ad or something new from SE.
It was just an ad, nothing to do with SE.