Well, the question I am proposing here is not whether or not Ryo is capable of murdering Longsun Zhao, I am asking how would you feel if the story did go down that route. Besides, there are a couple of ways I can think of in which Ryo kills him. Especially when you consider that Shenmue is supposed to be a role-playing game version of Virtua Fighter.
First, perhaps Ryo finds and trains in some sort of anti-Koen-ken style that was long forgotten via texts or an instructor. In the second scenario, since Longsun Zhao is essentially Lau-chan in this universe, perhaps he is also slowly dying of a terminal illness and wanted revenge for his father before he dies. Or finally, Ryo just decides to grab a .45 and deal with him that way.
I agree with what
@Revan said as it would contradict the themes of what Shenmue is trying to convey. However, that is why I added in that scenario where Ryo feels empty and despondent after killing Lan-Di. To nail home the lesson of the futility of revenge and then spend the rest of the story trying to atone for his sins. After all, sometimes the only way one learns a lesson is the hard way or experiencing it first-hand.