...does he die?
I know in the next film Bourne tells Marie's brother that he killed the man who killed his sister and he does look like he takes his last breath when Bourne's pointing his gun at him.
But is it stated anywhere that Kirill is actually dead as it kind of is open to interpretation (at least to me).
I do not think he died, just left in pretty bad shape.
The comment to Marie's brother in Ultimatum could also apply to Ward Abbott (as he ordered the hit on them in Goa) rather than Kirill.
I think it is left for the viewer to decide what they think, but in my opinion Kirill does not die from his injuries (the "last breath" could be a sigh of relief as he does look Bourne in the eye while he is holding the gun at him, waiting for him to pull the trigger, then Bourne just walks off).... how would Bourne know he is dead as he walked away before he had a chance to be sure.
As said, the comment to Maries brother was probably more likely Abbott as Bourne knows Kirill was just the same as he was, following orders.