@Thomas
It's a live action RPG. You run into guys every so often on the street and get in fights. One thing that was not apparent in the demos is that you can always grind, and do subquests, to level up. And you also have the ability to buy food to replenish your health. The demo was terrible, don't rely on the demo to make your decision.
If you like RPGs and fighting games, the game is a blend of both. I loved the game (and it was the first Yakuza I ever played). I got no sleep for two solid weeks because I couldn't stop playing it. I stayed up until 5 AM on the weekends playing.