I have a website with a bunch of videos from an API which sends me the URL of the video, so not the <embed> nor the <iframe>. What I do is to play them with the HTML5 video element.
Would it be a good idea (SEO speaking) to create those snippets? As videos are not mine and may be in other websites as well, I don't know if is allowed or even a good idea to put them.
Yes, it’s a good idea.
Structured data is not only useful for content you authored. It allows you to say anything about anything (see Semantic Web and Linked Data).
You provide this video for your human visitors, possibly showing its title and other metadata. Why not also provide this data in a way that machines can easier understand?
Or in other words: Any entity (an object, an organization, a person, a concept, a work, an idea, etc.) you have content about on your page is a possible candidate for providing structured data about it.
FWIW, here’s a related Google Webmasters video about this:
Should I add schema.org markup on my videos even if they're on YouTube?
Rich snippets are automatically added to SERPs for video results from YouTube. Is it recommended to add schema video markup onsite in order to get your page w/embedded video to rank in SERPs in addition to the YouTube result, or is this redundant?
tl;dw: Yes, please get them to add the markup.
