NextGEN Facebook does not (currently) include og:video and og:audio tags. It's not that I didn't want to include them, I just didn't think about it. ;-)
There are a lot of ways to embed videos and audio files within content, so this could be a challenge... If you can give me the URL to a specific page, I can have a look at the source and see if I can include it in the next version.
As for why Facebook is / is not picking up your video file, it probably depends on how the video is embedded. Facebook reads the OG meta tags when available, but it also looks at the content. Your first site must embed the video using a different technique... Have a look at the source from both pages and see what the difference might be.
Alternatively, give me both URLs and I'll have a look. ;-)