There are arcade style points while playing. They are rewarded for doing anything with style or doing pretty much anything at all. A lot of the points come along with descriptions that are often descriptive, snarky, or both.
You get points for kicking guys off cliffs, for whipping guys into the air (and exploding barrels next to them), and for finding out the way to kill difficult enemies.
There are very cheesy lines and slow motion kills but it all adds to the aesthetic which simply just seems to be, to have fun.
Look for more on BulletStorm later on.