Yakuza is set in the future of ShenmueKiryu is Ryo Hazuki after he is adopted by a Yakuza after the death of his father. He even has an arch enemy who is a Chinese mob boss in Lau Ka Long. The timing even works, since Shenmue is set Twenty Minutes into the Past.
Yakuza is set in an alternate universe as GungraveGungrave's universe is one where the cast of Yakuza is transplanted into America, hence the different names, of course. Brandon Heat is clearly Kazuma Kiryu, orphan effectively raised by a high-up gangster. Heck, he's even named for his counterpart's Limit Break. They both have a spectacular rise in a mob family, only for things to fall apart at the end due to their best friend killing the leader of the mob, though they do wind up coming back stronger than ever. Also, compare Maria/Mika. Both of them are the main character's Morality Pet, and they're the daughter of the main's love interest, who married a powerful older man when a relationship with the main character became impossible (Brandon for class reasons, Kazuma for that whole jail thing). That just seems like an oddly specific coincidence, unless something cosmic is at work here.