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Every time I have seen this happen it is due to duplicate content across various URL's or very thin content. Google doesn't tend to want to keep an index of the same page many times or many pages with little to nothing on them. If you didn't have duplicate or thin content problems and have cleaned up your error producing URL's then I'm not sure what to tell you. Someone will probably have to get into your GWT account to diagnose from there.

In short - no. Videos can appear for any in the SERPs - and it will vary dependent on the keyword in question. If you're struggling to get about 5, I suggest you probably just need to build more/better links to see substantial increases.