Even if we were to assume that Chauvin did not directly cause Floyd's death, he is still guilty of (at least) assault. Minneapolis use of force policy prohibits the use of a neck hold on someone who is less than actively resistant. When Floyd lost consciousness, it was no longer possible for him to actively resist Chauvin. Chauvin therefore clearly exceeded the authorized use of force and crossed the line into assault.
Chauvin's particular "crime" wasn't probable murder or assault. From what I has been reported, the face down, knee on neck, restraint position is not prohibited in Minneapolis but it is taught that "stomach down" it can be dangerous and must be used judiciously. In the circumstances, even if we fully accept the prosecutions portrayal of events, this was a largely understandable misjudgment and, at worst, grossly negligent use of an approved method of restraint.
According to the charge summaries:
As the two arresting officers tried to put Floyd in their squad car he resisted, stiffening up and falling to the ground. He told officers he didn't want to get in the car because he was claustrophobic.
Chauvin and Thao then arrived.
Then three of the officers made several attempts to get floyd into the backseat, he repeatedly resisted, now saying he could not breath. After physically struggling, they tried to get him into the car and made one final attempt.
Chauvin gave up and pulled him out of his position in the passenger seat, and Floyd went to the ground face down. At that point Chauvin placed his knee on his head and neck area, and two officers held his back and legs.
Floyd protested loudly, claiming (again) that he couldn't breath imploring "I'm about to die."
One officer noted "you are talking just fine", as Floyd continued to move. Lane asked about rolling him on his side, Chavin said no ' (he is) staying put were we got him. Lane then said something about worrying over Floyd's excited delirium (hyper aggression and unusual strength from drugs), and Chauvin said "that's why we have him on his stomach".
At 8:24:24 Floyd stopped moving. At 8:25:31 Floyd ceased to breath or speak. Lane suggest rolling on his side, , another officer checked floyds right wrist and said that he couldnt find a pulse. For two more minutes Chauvin held him under his knee.
Conclusion:
Most likely the officers believed the foam mouthed individual battling to stay out of the back seat of the police car was in a state of drug induced agitated or excited delirium. Apparently Chauvin decided the only way to get him under control and too cooperate was to use a restraint method that took the fight out of him. In the process, due to Chauvin's heart condition (and other factors) he may well have perceived that he was short of breath PRIOR to being restrained, which apparently was not due to a lack of breath.
Chauvin mistake and negligence was in not immediately stopping his restraint when told that there was no pulse, and then in not immediately rendering first aid. Although it was likely too late, three minutes of neck (or back) restraint AFTER all movement ceased, and two minute after he ceased to breath, was arguably grossly negligent and chargeable under second degree manslaughter (3rd degree murder in Minn.).
Whether or not that would "stick" will depend on several factors.