Don’t know exactly what you mean by video submission. If it’s about the additional video on YouTube, it doesn't really matter. The video can be proof of your work, so you would show your project being played in your DAW. However, it isn’t really necessary, since you need to upload screenshots of your project anyway (as proof). So how you’d make the video is up to you and your creativity. Same for other streaming platforms. However I would recommend, that your soundtrack is the same as your upload for the jam, since some people may only watch your additionaly provided links (like on YouTube or SoundCloud).
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That is quite an interesting approach. As for me, I wouldn’t bother if the video would be edited. Even in DAWs nothing is played in an one-shot. I would recommend recording your playing and take the best shots for a cohesive edit but keep in mind that it should be the same as your submission on itch.io (for sound). For screenshots use a photo of your gear, like seen on the video, and that’s it.