Why did these 'creatures' fight each other?

I haven't seen the movie yet; only the trailer where they make an appearance. Having read the book many times, though, I do know they are present there as well. In the book, the stone giants aren't battling, but instead are throwing rocks for fun, and (as you point out) are oblivious to any other creatures around them that might be affected by their game.

One could read their presence in the book as a sort of literary description of how, in a world of fantasy like middle-earth, devastating weather (like the dwarves and Bilbo encounter in the Misty Mountains) might be imagined. It makes sense to see their game of boulder throwing as serving a similar purpose in the movie.

There is a reference to them in the book but they were having a game in the book so only the screenwriters/Peter Jackson will be able to explain why they were feuding so violently in the movie.

I think its a change for dramatization, being that it would be a bit anticlimactic to have them merely frolicking. It just wouldn't have suited the mood of the movie. That's my assumption. It'd be nice to have there be an explanation of some sort in a DVD extra or something or maybe a mini film based off of Tom Bombadil's adventures adding in a moment where Tom sets off these giants to feuding to the death. Or perhaps as my girlfriend brilliantly suggests they are blaming each other for lightning strikes, and the feud just reaches a deadly climax during the unexpected journey!

In the source novel, their actions are described thusly;

When he peeped out in the lightning-flashes, he saw that across the valley the stone-giants were out and were hurling rocks at one another for a game, and catching them, and tossing them down into the darkness where they smashed among the trees far below, or splintered into little bits with a bang.

The film's commentary track (between Director Peter Jackson and Screenwriter Pippa Boyens) isn't any more enlightening than that. Commenting on why the giants are fighting...

PJ: Yeah, I always wondered why these giants dislike each other so much. It must be something very personal has gone on.

PB: Well, maybe it's in their nature.

[both laugh]

My theory is that the giants are the remnants of an ancient guardian race created by Morgoth to defend against the coming of Orome. The misty mountains were raised by Morgoth long before the first age of middle earth began. This was to hinder the riding of Orome (one of the Valar) and prevent the newly awakened elves from journeying west to beleriand and the sea beyond. Just a theory...