Pretty simple really. the sparkler is the fuse. It burns down into the explosive materal - which you can sort of see packed all around the sparkler. They called it a sparkler bomb, but that doesn't describe the explosive part, just the fuse part.
Might as well correct the record 6 years later - a sparkler bomb only requires sparklers. Packed together in a metal pipe as they showed, the reaction is chained and prevented from slowly escaping.
It's like the difference between igniting a thin layer of black powder laying in a bowl (a relatively slow release of heat and light) and igniting the same amount wadded up inside a rifle with the bullet immovably stuck (an exploding gun).
Here's what happens if you only loosely bind them with some tape. (warning: loud) http://www.youtube.com/watch?v=OX6L7rde5es