The plugin uses splash images.
Splash images are css backgrounds, which by definition do not have SEO relevant info (see http://christianheilmann.com/2009/02/25/so-how-do-you-add-alternative-text-to-background-images/ ), and therefore no way of adding alt text.
While not used by the plugin, the poster attribute does not offer alt text either, at least in the current html5 draft. See http://www.w3.org/html/wg/tracker/issues/142 (still postponed)
You’d probably be better off by creating video sitemaps anyway, where you could link the splash image to the <video:thumbnail_loc> element: https://support.google.com/webmasters/answer/80472?hl=en
The problem is that often or most times the image overlay is a significant part of the page content, the first picture after the logo in my case, but if it’s not registered as a picture with alt text Google will not rank it high in img search..
I see your point, but as I said, the html5 and css specs simply do not allow alt text for these elements.
Perhaps you can borrow this hidden image trick https://flowplayer.org/forum/#!/setup:pinnable-thumbnails/pinterest-does-not-support ; I have no idea though whether Google will parse it and how it affects SEO. But it’s worth a try.