Hmmm, so I did as you suggested and deactivated the plugin, then went into database and removed 2 related options I found in wp_options table (wpseo_video_xml_update, wpseo_video). Then, I reactivated the plugin, inserted my license key and tried a test by inserting a youtube video link in a post and hit update button. Nothing changed. I still do not see the “Video” tab in the SEO options.
After you deactivated the plugin, did you remove any other rows than the 2 I mentioned?