From the voice lines in Retribution we learned that Genji wanted to be able to walk again. This means that the injury Genji sustained severed his spine nerves, which is what causes you to become crippled.
We know the fight happened in Hanamura castle from the fact that Hanzo comes to the spot anually (despite the danger) to honor the spot his brother fell.
But if you look closely, you can see the banner has some blood stains and a cut. This strongly implies that Hanzo cut through Genji in order for him to slice the banner as well as his brother.
And in order for Genji’s Blackwatch skin to align, he was cut down from behind. His scars also indicate he received several cuts prior to the fatal blow.
It also explains why Genji had to become a cyborg to survive. Most of his body was most likely lost due to being cut in half.
In Heroes of the Storm, Hanzo also has additional dialogue with other Overwatch characters, saying “His brother betrayed his clan for Overwatch.” Genji had most likely already been recruited to Overwatch before being fatally injured and called for help at the start or during the fight, meaning Overwatch agents arrived just in the nick of time to save him from an otherwise fatal injury.
From the amount of regret and shame Hanzo felt after killing his brother, as well as the remorse Genji felt later on for his brother, it also seems that it was not Hanzo’s wish to kill Genji.
They were part of a criminal organization “The Shimada Clan” and Genji was to inherit his father’s criminal empire, but lived a dishonorable lifestyle as a “flamboyant playboy” which led to the clan wanting to kill him.
Given Hanzo’s large focus on “honor,” it’s most likely he choose to kill Genji himself in order to give his brother an “honorable death” with the chance to defend his own life instead of an assassination by the clan (poisoning/killed in his sleep/etc).
Genji also called Hanzo a coward (and not a traitor), that he choose to let the clan dictate his actions instead of making his own choice (e.g. fighting the clan and/or escaping with his brother).
Genji’s forgiveness of Hanzo comes down to the acceptance that his death was brought upon himself for his carefree choices in a very dangerous life (also reflected in Retribution: Genji comments he has no remorse for taking the life of criminals, likely because his criminal clan was responsible for his death).
It will be exciting to see where their story goes from here. Genji made a clear attempt to bring Hanzo into the fold in the animated cinematic “Dragons” and Hanzo’s “Cyborg” skin does imply that he might join Overwatch, but interactions with members of Talon also imply they have an interest in him (not a mutual one).