That's what this site is all about' isn't it? Figuring out how it works and marvel at the guy who thought of it first. Now we can reproduce it, but we're not the first.
Put your camera on a tripod. Have a moderate telelens, like maybe 100mm, at F2.8. Prefocus manually as close as possible. Open the shutter with bulb exposure (B) when the skyrocked is launched and turn the focus ring towards infinity quickly, when it bursts. That's how I would have tried it.
David Johnson, the photographer here.
The effect is quite simple:
I was using a 5D mark II with a 50mm lens. I had a neutral density filter, the light was too bright otherwise. Hold bulb mode when the fireworks was on it's way up, and when the explosion begins you quickly refocus. You can try starting out of focus and pulling inwards, or visa versa... both create bizarre effects!
As soon as I saw the first image I thought "Oh, turning the focus ring while the shutter's open, neat idea." Being close and using a 50mm lens helps the effect a lot.
Last time I had the opportunity to shoot fireworks, I was miles away and using a 180mm lens. It didn't occur to me to twist the focus ring during the exposure, but the effect wouldn't have been so dramatic, I think.