I know that I can use a NPAPI plugin with <embed> tag, but I was wondering is it possible to implement NPAPI plugin that will be called for <video> tag?
No, there's no automatic fallback from <video> to NPAPI plugins. If you wanted to use an NPAPI plugin to handle <video> you'd need to make an extension for each browser that would rewrite <video> tags on pages to be <embed>/<object> instead.