Like the others said, the quantity of light is the major concern. If the games you are concerned about photographing are during the day, then you can get by pretty easily with a long-zoom PnS. If they're at night... well, keep your expectations realistic.

For low-light ability, the big-sensor Fujis are untouched in the PnS arena, but they don't have image stabilization, but the dramatic improvement in quality over the others can outweigh that. Similarly, the daytime parades at Disney are easy, but SpectroMagic can be extremely difficult.
For fireworks, most any camera can do very well, a tripod/Gorillapod/Clamperpod is more important than the type of camera (within reason, of course.) Ideal is a camera that has a "bulb" mode (takes a picture for as long as you hold with the shutter) with a remote shutter release, so you don't shake the camera as you take the photo. You can still do pretty well with by manually setting a long-ish exposure (2-5 seconds, probably) with a 2-second delay after pressing the shutter, to give the camera time to stop shaking from you pressing the shutter.
Most current PnSs will be a lot more responsive than what you're used to if your camera was a few years old. You may want to try some in the store, but by and large, shutter lag isn't nearly the problem that it used to be. However, don't be sold on megapixels, more megapixels don't guarantee a better picture, often it's the exact opposite.