It does have a story, there are some story recaps on youtube if you want to check it out.

Guilty Gear not even getting mentioned once is criminal, the entire franchise has amazing music, to the point where the fanbase and the fighting game community likes to joke that they get a free game with every new music album whenever a new game comes out.

To add to this, basically everything Daisuke Ishiwatari makes, who is mainly responsible for almost everything about the game.