I recently wrote about some Gallery3 modules that I find useful. One Idea that came up to my mind was to implement html5 video in Galley 3. So I did that. The result is not that spectacular, but can be found and downloaded from GitHub. The big advantage compared to other video.js or flash based solutions is a better support for mobile devices.
The installation is simple, just copy the module to the modules folder of your Gallery3 installation and enable it in the Admin/Modules panel.
You can see the result for example in my Gallery, e.g. in the Grass rendering video page. A precondition is of course your browser supports the video tag.