I think it's possible to believe Scorpion wanted revenge for Bi-Han killing him, while also believing Bi-Han was killed unjustly. The two concepts aren't mutually exclusive. Revenge isn't inherently just. In fact how many times have you heard this line in a movie or cop drama: "What you want is revenge, not justice!" ... the two concepts are frequently illustrated as being at odds with one another.
I do think it's valid to state he was more motivated by the deaths of his clan and family, but for the sake of arguement, lets say he wanted revenge for himself too (as his MK1 bio states he did)...
Bi-Han & Hanzo were in rival clans which both accept the use of deadly force and found themselves brought into direct competition with one another in MK Mythologies. As has been pointed out out, if Bi-Han hadn't killed Hanzo, Hanzo might very well have killed Bi-Han. Bi-Han defeated him in fair kombat and chose not to spare his life. Could he have? Maybe. But it's not as if we know for certain Hanzo would have done the same, and it's not as if Hanzo didn't know what he was getting into, or what line of work he was in. These me know their job could mean their lives. What sets Scorpion off is the job should never have meant the lives of his family as well. I would not call the circumstances for Hanzo's death cold-blooded murder. He just lost a fight which (like many fights in this franchise) both men knew could likely mean their death.
Just because Scorpion wanted revenge for that, that doesn't make revenge just. The fact that he was further duped into believing Bi-Han killed his wife and family to fuel his motivation, makes it all the more unjust.
