Thanks. Non-linear, I get. So there must be an equivalent of a DAW for video, just with tracks that are video with audio, instead of just audio?
That's essentially it, Matt. I've worked some in Cyberlink's video editing software. I think straight out of the box, you could learn to create something like this relatively easily with their built-in capabilities. But, like an audio DAW, there are myriad Fx available 3rd party.
Most likely there was a separate audio track mixed with the videos. It's possible (likely) the video clips contained sound if only to help with synching, but ultimately there was a single master audio track.
The main point is...thinking of it as a Video DAW is the right way to think of it. That helped me learn the software (which isn't terribly hard) more easily than I might have otherwise, having been messing with audio for some time.
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I'll throw this in for free. BIAB "save as video" feature (and the apparently abandoned Video Real Tracks feature) may get you a long way. I was looking into it back when I had time, but haven't thought about it much lately until reading your post.