[jerf]

"They both use shockwaves to smother the fire."

That speaker isn't emitting "shockwaves": http://en.wikipedia.org/wiki/Shock_wave That's obviously a standard speaker cone and is entirely subsonic.

I would have to agree that a true high-explosive shockwave is a beast of a different color.

[Trisell]

Using dynamite to 'blow out' the fire by forcing the burning fuel and oxygen away from the fuel source.

It sounds to me like they were using the explosives to essentially force a change in fuel air mixture. Essentially the same idea as when the wind blows out your lighter or match. Just way more fun, because explosives. :D

Edit: Quote is from Oil Wikipedia Article above.