In the gaming world there is a balance. In order for there to be a in depth story, you need to sacrifice interactivity. And in you are going to be interactive, you will no doubt lose much of the deep story. In making a game you try to balance this out as much as you can. Unfortunately Art of Fighting sacrifices too much of the game for a story.
Perhaps if the game controlled better, giving a more intense experience, Art of Fighting would be a better game. However, the game experience feels more like a novelty than a game with structure. The only good that came out of the game was a new (for the time) camera effect that zoomed in, and zoomed out depending on how close the fighters are to each other. However, even that wasn't used well until Samurai Shodown.
One other notable oddity to the game is the "special move meter" ... it's a bar that tells you how many special moves you can do. It would add to the strategy of the game, if the moves weren't so hard to pull off.
This game is a mess. It's one player mode is not worth playing, as it has a simple story mode, that really isn't interesting at all. In fact, it really reminds me of a more mature version of the Fatal Fury story. It's a mafia story, and it's like all other mafia stories. The two player mode at least lets you play as eight people, but again, none of the characters have more than three moves, and most of the technique is taken up with snazzy camera effects. Not at all fun to play. It's really hard to recommend this game to anybody except for people that must own all fighting games. It's comparable to Rise of the Robots.